Do NowDo Now

Two people exert a 10 Newton force Two people exert a 10 Newton force for 2 meters Person 1 exerts the for 2 meters Person 1 exerts the force at a 50 degree angle Calculate force at a 50 degree angle Calculate the work done on the box by each the work done on the box by each personperson

Person 1 Person 2

W = Fdcosθ = (10N)(2m)cos50˚

= 129 J

W = Fdcosθ = (10N)(2m)cos0˚

= 20 J

Net WorkNet Work 12) An object is pulled by a 20N force 12) An object is pulled by a 20N force

due east for 5 meters and then due due east for 5 meters and then due north by the same force for 3 meters north by the same force for 3 meters How much work was done How much work was done

5m

3m

Note The net work is related to the path traveledIt is NOT related to the resultant displacement

R

W1 = (20N)(5m) = 100 J

WT= W2 + W3 = 160 J

W2 = (20N)(3m) = 60 J

LiftingLifting 14) I decide to get my pet frog to 14) I decide to get my pet frog to

do a little weight lifting (but Irsquom do a little weight lifting (but Irsquom going to start him off slow) He going to start him off slow) He lifts 2 kg up from the floor over lifts 2 kg up from the floor over his head 2 cm How much work his head 2 cm How much work did he dodid he do

W = Fd cosθFlift = Weight

Flift = mg = 2kg(98ms2)

Weight

Flift = 196 N

W = (196N)(002m)

W = 0392 J

Why is it easier to lift the boulder with this simple machine than to pick it up directlyDoes it take less Work to lift the boulder this way

Input Work = Output Work

W= 1N x 4m W= 4N x 1m

4 J 4 J

4 m

1 m

Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput

Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make

work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs

hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo

c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power

Compound pulleys Compound pulleys reduce the force needed reduce the force needed

to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter

W = Fd

W = (100N)(1m)

W = 100 J

W = Fd100 J = (25N)d

d = (100J)(25N)

d = 4m

15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless

20kg

F

x

Begin by calculating the force necessary tomove the object

gF mg220 98g

mF kgs

196gF N

gFW F d

196 50W N m 9800W J

GraphsGraphs 16) What does the slope of a 16) What does the slope of a

Force versus Displacement graph Force versus Displacement graph representrepresent

Forc

e (

N)

Displacement (m)

yslope

x

Fslope

d

FNothing

d

1)Write down a formula that uses the variables onthe x and y axis

W F d

GraphsGraphs 17) What does the area under the 17) What does the area under the

curve representcurve represent

Forc

e (

N)

AREA

Displacement (m)

How do you find the area

A length height

A displacement force

A F d

W F d

Area Work

W F d

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

Net WorkNet Work 12) An object is pulled by a 20N force 12) An object is pulled by a 20N force

due east for 5 meters and then due due east for 5 meters and then due north by the same force for 3 meters north by the same force for 3 meters How much work was done How much work was done

5m

3m

Note The net work is related to the path traveledIt is NOT related to the resultant displacement

R

W1 = (20N)(5m) = 100 J

WT= W2 + W3 = 160 J

W2 = (20N)(3m) = 60 J

LiftingLifting 14) I decide to get my pet frog to 14) I decide to get my pet frog to

do a little weight lifting (but Irsquom do a little weight lifting (but Irsquom going to start him off slow) He going to start him off slow) He lifts 2 kg up from the floor over lifts 2 kg up from the floor over his head 2 cm How much work his head 2 cm How much work did he dodid he do

W = Fd cosθFlift = Weight

Flift = mg = 2kg(98ms2)

Weight

Flift = 196 N

W = (196N)(002m)

W = 0392 J

Why is it easier to lift the boulder with this simple machine than to pick it up directlyDoes it take less Work to lift the boulder this way

Input Work = Output Work

W= 1N x 4m W= 4N x 1m

4 J 4 J

4 m

1 m

Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput

Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make

work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs

hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo

c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power

Compound pulleys Compound pulleys reduce the force needed reduce the force needed

to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter

W = Fd

W = (100N)(1m)

W = 100 J

W = Fd100 J = (25N)d

d = (100J)(25N)

d = 4m

15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless

20kg

F

x

Begin by calculating the force necessary tomove the object

gF mg220 98g

mF kgs

196gF N

gFW F d

196 50W N m 9800W J

GraphsGraphs 16) What does the slope of a 16) What does the slope of a

Force versus Displacement graph Force versus Displacement graph representrepresent

Forc

e (

N)

Displacement (m)

yslope

x

Fslope

d

FNothing

d

1)Write down a formula that uses the variables onthe x and y axis

W F d

GraphsGraphs 17) What does the area under the 17) What does the area under the

curve representcurve represent

Forc

e (

N)

AREA

Displacement (m)

How do you find the area

A length height

A displacement force

A F d

W F d

Area Work

W F d

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

LiftingLifting 14) I decide to get my pet frog to 14) I decide to get my pet frog to

do a little weight lifting (but Irsquom do a little weight lifting (but Irsquom going to start him off slow) He going to start him off slow) He lifts 2 kg up from the floor over lifts 2 kg up from the floor over his head 2 cm How much work his head 2 cm How much work did he dodid he do

W = Fd cosθFlift = Weight

Flift = mg = 2kg(98ms2)

Weight

Flift = 196 N

W = (196N)(002m)

W = 0392 J

Why is it easier to lift the boulder with this simple machine than to pick it up directlyDoes it take less Work to lift the boulder this way

Input Work = Output Work

W= 1N x 4m W= 4N x 1m

4 J 4 J

4 m

1 m

Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput

Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make

work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs

hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo

c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power

Compound pulleys Compound pulleys reduce the force needed reduce the force needed

to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter

W = Fd

W = (100N)(1m)

W = 100 J

W = Fd100 J = (25N)d

d = (100J)(25N)

d = 4m

15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless

20kg

F

x

Begin by calculating the force necessary tomove the object

gF mg220 98g

mF kgs

196gF N

gFW F d

196 50W N m 9800W J

GraphsGraphs 16) What does the slope of a 16) What does the slope of a

Force versus Displacement graph Force versus Displacement graph representrepresent

Forc

e (

N)

Displacement (m)

yslope

x

Fslope

d

FNothing

d

1)Write down a formula that uses the variables onthe x and y axis

W F d

GraphsGraphs 17) What does the area under the 17) What does the area under the

curve representcurve represent

Forc

e (

N)

AREA

Displacement (m)

How do you find the area

A length height

A displacement force

A F d

W F d

Area Work

W F d

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

Why is it easier to lift the boulder with this simple machine than to pick it up directlyDoes it take less Work to lift the boulder this way

Input Work = Output Work

W= 1N x 4m W= 4N x 1m

4 J 4 J

4 m

1 m

Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput

Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make

work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs

hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo

c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power

Compound pulleys Compound pulleys reduce the force needed reduce the force needed

to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter

W = Fd

W = (100N)(1m)

W = 100 J

W = Fd100 J = (25N)d

d = (100J)(25N)

d = 4m

15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless

20kg

F

x

Begin by calculating the force necessary tomove the object

gF mg220 98g

mF kgs

196gF N

gFW F d

196 50W N m 9800W J

GraphsGraphs 16) What does the slope of a 16) What does the slope of a

Force versus Displacement graph Force versus Displacement graph representrepresent

Forc

e (

N)

Displacement (m)

yslope

x

Fslope

d

FNothing

d

1)Write down a formula that uses the variables onthe x and y axis

W F d

GraphsGraphs 17) What does the area under the 17) What does the area under the

curve representcurve represent

Forc

e (

N)

AREA

Displacement (m)

How do you find the area

A length height

A displacement force

A F d

W F d

Area Work

W F d

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

Input Work = Output Work

W= 1N x 4m W= 4N x 1m

4 J 4 J

4 m

1 m

Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput

Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make

work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs

hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo

c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power

Compound pulleys Compound pulleys reduce the force needed reduce the force needed

to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter

W = Fd

W = (100N)(1m)

W = 100 J

W = Fd100 J = (25N)d

d = (100J)(25N)

d = 4m

15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless

20kg

F

x

Begin by calculating the force necessary tomove the object

gF mg220 98g

mF kgs

196gF N

gFW F d

196 50W N m 9800W J

GraphsGraphs 16) What does the slope of a 16) What does the slope of a

Force versus Displacement graph Force versus Displacement graph representrepresent

Forc

e (

N)

Displacement (m)

yslope

x

Fslope

d

FNothing

d

1)Write down a formula that uses the variables onthe x and y axis

W F d

GraphsGraphs 17) What does the area under the 17) What does the area under the

curve representcurve represent

Forc

e (

N)

AREA

Displacement (m)

How do you find the area

A length height

A displacement force

A F d

W F d

Area Work

W F d

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput

Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make

work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs

hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo

c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power

Compound pulleys Compound pulleys reduce the force needed reduce the force needed

to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter

W = Fd

W = (100N)(1m)

W = 100 J

W = Fd100 J = (25N)d

d = (100J)(25N)

d = 4m

15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless

20kg

F

x

Begin by calculating the force necessary tomove the object

gF mg220 98g

mF kgs

196gF N

gFW F d

196 50W N m 9800W J

GraphsGraphs 16) What does the slope of a 16) What does the slope of a

Force versus Displacement graph Force versus Displacement graph representrepresent

Forc

e (

N)

Displacement (m)

yslope

x

Fslope

d

FNothing

d

1)Write down a formula that uses the variables onthe x and y axis

W F d

GraphsGraphs 17) What does the area under the 17) What does the area under the

curve representcurve represent

Forc

e (

N)

AREA

Displacement (m)

How do you find the area

A length height

A displacement force

A F d

W F d

Area Work

W F d

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make

work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs

hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo

c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power

Compound pulleys Compound pulleys reduce the force needed reduce the force needed

to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter

W = Fd

W = (100N)(1m)

W = 100 J

W = Fd100 J = (25N)d

d = (100J)(25N)

d = 4m

15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless

20kg

F

x

Begin by calculating the force necessary tomove the object

gF mg220 98g

mF kgs

196gF N

gFW F d

196 50W N m 9800W J

GraphsGraphs 16) What does the slope of a 16) What does the slope of a

Force versus Displacement graph Force versus Displacement graph representrepresent

Forc

e (

N)

Displacement (m)

yslope

x

Fslope

d

FNothing

d

1)Write down a formula that uses the variables onthe x and y axis

W F d

GraphsGraphs 17) What does the area under the 17) What does the area under the

curve representcurve represent

Forc

e (

N)

AREA

Displacement (m)

How do you find the area

A length height

A displacement force

A F d

W F d

Area Work

W F d

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

Compound pulleys Compound pulleys reduce the force needed reduce the force needed

to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter

W = Fd

W = (100N)(1m)

W = 100 J

W = Fd100 J = (25N)d

d = (100J)(25N)

d = 4m

15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless

20kg

F

x

Begin by calculating the force necessary tomove the object

gF mg220 98g

mF kgs

196gF N

gFW F d

196 50W N m 9800W J

GraphsGraphs 16) What does the slope of a 16) What does the slope of a

Force versus Displacement graph Force versus Displacement graph representrepresent

Forc

e (

N)

Displacement (m)

yslope

x

Fslope

d

FNothing

d

1)Write down a formula that uses the variables onthe x and y axis

W F d

GraphsGraphs 17) What does the area under the 17) What does the area under the

curve representcurve represent

Forc

e (

N)

AREA

Displacement (m)

How do you find the area

A length height

A displacement force

A F d

W F d

Area Work

W F d

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless

20kg

F

x

Begin by calculating the force necessary tomove the object

gF mg220 98g

mF kgs

196gF N

gFW F d

196 50W N m 9800W J

GraphsGraphs 16) What does the slope of a 16) What does the slope of a

Force versus Displacement graph Force versus Displacement graph representrepresent

Forc

e (

N)

Displacement (m)

yslope

x

Fslope

d

FNothing

d

1)Write down a formula that uses the variables onthe x and y axis

W F d

GraphsGraphs 17) What does the area under the 17) What does the area under the

curve representcurve represent

Forc

e (

N)

AREA

Displacement (m)

How do you find the area

A length height

A displacement force

A F d

W F d

Area Work

W F d

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

GraphsGraphs 16) What does the slope of a 16) What does the slope of a

Force versus Displacement graph Force versus Displacement graph representrepresent

Forc

e (

N)

Displacement (m)

yslope

x

Fslope

d

FNothing

d

1)Write down a formula that uses the variables onthe x and y axis

W F d

GraphsGraphs 17) What does the area under the 17) What does the area under the

curve representcurve represent

Forc

e (

N)

AREA

Displacement (m)

How do you find the area

A length height

A displacement force

A F d

W F d

Area Work

W F d

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

GraphsGraphs 17) What does the area under the 17) What does the area under the

curve representcurve represent

Forc

e (

N)

AREA

Displacement (m)

How do you find the area

A length height

A displacement force

A F d

W F d

Area Work

W F d

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

GraphsGraphs

18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75

A F d

W F d

Area Work

5 11W N m

55W J

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an

object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object

Forc

e (

N)

Displacement (m)

5

10

2 4 6 8 10 12

25

75 12A b h

Area Work

1 10 752A m N

375A N m Work

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

What is PowerWhat is Power

Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed

= F v

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

Units of PowerUnits of Power

20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in

secondsseconds

WP

t

JoulesP

Second 1

11

Joulewatt

Second

Power is measured in WattsWe will examine mechanical power rather than

Electrical power

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

PowerPower 21) What are some common 21) What are some common

devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power

Examples Motors heaters and Examples Motors heaters and other machinesother machines

22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

PowerPower

23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts

WP

t

100075

JW

t

133t s

1000

75

Given

W J

P W

t

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20

watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d

Pt t

10 5020

N mW

t

10 50

20

N mt

W

25t s

20

50

10

Given

P W

d m

F N

t

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs

W F dP

t t

266 98 6468

mkg N

s

The force necessary to climb the ladder is equalto the weight of the student

gF mg

F dP

t

6468 14

44

N mP

s

2058W

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

ConceptualConceptual

27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement

F dP

t

dvelocity

t P F v

As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force

Answer Power Increases

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

PowerPower

28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

GraphsGraphs 29) What does the slope of a 29) What does the slope of a

Work vs Time graph representWork vs Time graph represent

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75 yslope

x

Wslope

t

Wslope Power

t

1)Write down a formula that uses the variables onthe x and y axis W

Pt

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

GraphGraph 30) How much power is 30) How much power is

developed by the system developed by the system represented by the graph belowrepresented by the graph below

Work

(J)

Time s

5

10

2 4 6 8 10 12

25

75

Wslope Power

t

75 0

10 0

J jPower

s s

075P W

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley

31) What is the power of the 31) What is the power of the Electric motorElectric motor

motor

1000kg

d=10mt = 20seconds

F dP

t

21000 98mF kgs

9800 10

20

N mP

s

4900P Watts

Pulley