Unbalanced (or will it be balanced?) forces exercise

This exercise involves the class being split in two even teams of equal strength outside.

Mass and Weight

Mass – measured in kilograms (kg) this is the amount of matter in an object

Weight – (measured in newtons). Weight is the force due to gravity acting on a mass.

Force (measured in Newtons symbol N)

A force is something which can change the motion (speed or direction) of an object.

Balanced forces – the object is stationary or at constant speed

Unbalanced forces – accelerate,deccelerate or change direction of an object

Force W(N) = mass(kg) x force due to gravity (g)

often written as the formula F = mg

Work out the weight of a 10Kg bag of potatoes.

weight of potatoes = 10kg x 10 N/kg

= 100 N

Finding the weight of an object.

The force due to gravity is 10 Nkg-1 (a constant with symbol g)

Task: Working out your weight

Use the scales to find your mass in kgs

Calculate your weight in newtons using the formula F =mg

What is the weight of

500g of butter?

2.3kg of cheese?

500mg panadol tablet ?

5 Newtons

23 Newtons

0.0005kg x 10 = 0.005N

Work out the weight of a 10kg bag of potatoes on the moon.

weight of potatoes = 10kg x 6 Nkg-1

= 60 N

Finding the weight of an object on the moon.

The force due to gravity on the moon is 6Nkg-1

Exercise – Finding your Force Weight on the Earth and moon –use the bathroom scales to fill in the table

Mass (kg) Weight on earth (N)

Weight on the moon (N)

Starter read page 114 Science to 16

• Write the title force and mass

• Write answers to questions on page 115 using full sentences

Force Diagrams

On diagrams forces are drawn with arrows indicating the direction of the force

The length of the arrows indicate the strength of the force

Forces acting on an object – you must be able to label these

Thrust Friction or drag

support

weight

When forces are balanced (ie the opposing arrows are the same size)………finish the sentence

..the object is either stationary or moving at a constant speed

Friction always opposes motion

Forces acting on an object include

Thrust – makes the object move

Friction – opposes motion

Weight - pull of gravity

Support – upwards push

Force Facts

In the absence of friction a moving object keeps on moving

When a force is applied to a stationary object and makes it move, the object gains kinetic energy

Complete cyclist question 6 on sheet – analysing force diagrams

What causes motion?

• Complete yr 11 yellow workbook page 194

How would you describe and show the unbalanced force acting on the bike below?

20000N 10000N

4000N

4000N

Forces can be added or subtracted

Net force 10000N

Acceleration

Vector arrows are used to show the size and direction of a net force

100N 100N

1000N

900N

What is the net downward force?

Describe the motion of the parachutist

10N

Label this force

Friction can be helpful or a nusiance

List areas where friction is helpful

List areas where friction is problem

Finding the friction force of different Surfaces – Force is measured by a force meter in Newtons (N). In this activity we measure the force required to pull blocks with different surfaces over a range of different surfaces

Draw this grid in your book

Block Surface Force meter reading

smooth table

smooth carpet

smooth lino

rough table

rough carpet

rough lino

Distance /Time /Speed/Acceleration

Speed is used to describe how fast something is moving

Speed is the distance travelled by an object per unit of time

Distance/Time /Speed notes

d = distance (m)

t = time (s)

v = speed/velocity (ms-1)

These are combined in the following equation to give the formula for the average velocity or speed.

t

d V(av)

d

V t

X

Task: find the formula for:

V = d = t =

This triangle can help you to remember the correct formula

t

d x tV

vd

The speed limit outside of a school is 50km/hr

A snails speed is 4 millimetres per second

A world class sprinter runs with a speed of 10 metres per second

The Unit of speed (aka velocity) depends on the units used to measure distance and time eg

The Bugati Vernon has a top speed of 400km/hr

What is its speed in metres per second?

Hint convert km to metres and 1 hour to seconds!

1hour = 60minutes and each minute has 60 seconds

To find speed (or V) we need distance in metres and time in seconds

The Bugati Vernon has a top speed of 400km/hr

What is its speed in metres per second?

1hour = 60minutes and each minute has 60 seconds

So 1 hour = 60min x 60 sec this = 3600s

The Bugati Vernon has a top speed of 400km/hr

What is its speed in metres per second?

11.1113600

400000

msvsm

v

td

v

t

d V(av)

find the following

1. What is the speed of a man who walks 300 metres in 120 seconds?

1. What is the speed of a man who walks 300 metres in 120 seconds?

td

V(av)

1-2.5ms

120s

300m V(av)

Toy Speeds

Car Name distance time (s) Speed d/t

1 1m 1.29s 0.78m/s

2 1m 1.4s 0.71m/s

3 1m 1.3 0.76m/s

28 1m 1.09s 0.92m/s

4 1m 1.12s 0.89m/s

Using one car from the front desk measure the speed of it over one metre.

Draw the following table in your books.

Fill in the distance, time and speed columns making sure you include the correct units.

1. What is the speed of a cyclist who rides 1000 metres in 150 seconds?

td

V(av)

1-6.6ms

150s 1000m

V(av)

write this in your book

1. What is the distance in metres covered by a motorcyclist who rides at 100kmhr-1 for 180 minutes?

write this in your book

d = V x t

= 100 kmhr-1 x 3hr

= 300km

= 300000 m

Distance time graphs

d

(m)

t (s)

Stopped/stationary

t (s)

d

(m)

constant

speed

Draw the distance time graphs and describe the motion of each object.

Note the greater the slope the faster the speed

t (s)

Slower constant speed d

(m)

t (s)

d

(m)

accelerating

d

t

ab

c Draw the graph

A man drives 80 km to Ashburton in 1hour and 10 minutes what is his average speed in m/s?

Show all your working and a formula.

Copy and complete the following

The man had the fastest constant speed at point __

The man got petrol at point ____

Love him or hate him Lance Armstrong is arguably one of the best cyclists in the world, having won a record 6 Tour de France races. He achieved the record for this race by winning the event 7 times in 2005!!

The first stage of the 92nd Tour de France is

the 19km individual time trial the top two results

are:

1. Dave Zabriskie (USA ) in 20min 51 sec

2. Lance Armstrong (USA ) in 20min 53 sec

Questions

What was the average speed (ms-1) of

Dave Zabriskie ?

Dave Zabriskie (USA ) competed the 19 km in 20min

51 sec

Convert kilometers to metres and minutes to seconds

19km = 19000m 19min 51sec = 1251 sec

Use formula to find speed

fig) sig 4(

1-15.19ms

1251s

19000m V(av)

t

d(av)V

What was Lance Armstrong’s average speed in metres per second?

Lance Armstrong (USA ) completed the 19km in 20min 53 sec

fig) sig (4

1-15.16ms

1253s

19000m V(av)

t

d(av)V

If Lance Armstrong could maintain this speed for one

Hour what distance would he have traveled?

(Give your answer in kilometers and metres)

v

fig) sig (4 km 54.58 or m 54,576 d

3600sx 15.16ms d

t x vd

rearrangedt

dv

1-

Finish the questions on work sheet one

K

P

1 2 3 4 5 6 7 8 9 10

t (s)

d

(m)

Finding speed from a distance time graph

t)( in time change

d)(distancein change K section of speed average

0

10

20

30

40

50

60

1-ms 5.7 (K) speed

4s

m30 (K) speed

t

d (K) speed

Task

Work out the speed for section P

d

T

K

P

1 2 3 4 5 6 7 8 9 10

t (s)

d

(m)

Finding the average speed of Section P

t)( in time change

d)(distancein change Psection of speed average

0

10

20

30

40

50

60

d

T

Speed / Time / Acceleration

• V = speed / velocity (ms-1)• t = time (s)• a = acceleration (ms-2)

time in change

velocity in changea

time in changevelocity start - velocity final

a

also written as:

∆V

a ∆t

X

Calculate the acceleration of a car if changes speed from 20m/s to 50 m/s in 3 seconds

time in changevelocity start - velocity final

a

2-

-1-1

ms10a

seconds 3

20ms - 50ms

a

A car travels for 320 kms at 80km/hr how long did it take him to travel the distance?

v

dt

80km/hr

320kmt

t = 4 hours

speed / time graphs

V

(ms-1)

t (s)

constant speed

t (s)

acceleration

Draw the acceleration time / graphs and describe the motion of each object.

t (s)

V

(ms-1)

V

(ms-1)

decceleration or negative acceleration

P

2 4 6 8 10 12 14 16 18 20

t (s)

V

(ms-1)

Finding the acceleration from a speed/time graph

Find the acceleration of Section Z

0

10

20

30

40

50

60

VZ

T

0

10

20

30

40

50

60

70

0 1 2 3 4 5Time (s)

Motion of a cricket ball

While playing in the Cricket World Cup, a New Zealand batsman hit the ball along the ground to the boundary for four runs. The following graph shows the motion of the ball as it rolled along the ground.

1. (a) What was the total distance travelled by the cricket ball?_____________________________________________________(__)m (A)

(b) Calculate the average speed of the ball ______________________________________________________________________________________________________________________________________________________________________________________________________average speed =____ms-1 (A)

Force mass and acceleration

When two opposing forces are not equal, they are said to be unbalanced. If an unbalanced force is applied to an object, the object will accelerate. The amount of acceleration depends on the size of the mass and the size of the force.

Force mass and acceleration are related by the formula:

ma F

F

m a

Where:

F = force (N)

m = mass (kg)

a = acceleration (ms-2)

A force of 500N is used to accelerate a 2kg object. What is the acceleration of the object?

a = 250 ms -2

m

Fa

2kg

500Na

Example 1

An object accelerates at 7.5ms-2 when a force of 15000 N is used to accelerate it. What is the mass of the object?

m = 2000 kg

Example 2

2-7.5ms

15000Nm

a

Fm

0

10

20

30

40

50

60

70

0 1 2 3 4 5Time (s)

Motion of a cricket ball

While playing in the Cricket World Cup, a New Zealand batsman hit the ball along the ground to the boundary for four runs. The following graph shows the motion of the ball as it rolled along the ground.

1. (a) What was the total distance travelled by the cricket ball?_____________________________________________________(__)m (A)

(b) Calculate the average speed of the ball ______________________________________________________________________________________________________________________________________________________________________________________________________average speed =____ms-1 (A)

1c. The ball was initially travelling at 23 ms-1 when it was first hit by the batsman and slowed to 1 ms-1 by the time it crossed the boundary.

Calculate the deceleration of the ball as it rolled across the grass____________________________________________________________________

________________________________________________________________________________deceleration =( )unit (A/M)

0

10

20

30

40

50

60

70

0 1 2 3 4 5Time (s)

Motion of a cricket ball

2 (a) Name the force that slows the balls speed as it rolls across the grass.

___________________________________________________(A)

The cricket ball used in One Day International cricket has a mass of 0.163 kg.

(b) Use your answer from 1 (c) on the previous page to calculate the net force slowing the ball down.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Net Force =( )unit(A/M)(c) Draw and label arrows on the following diagram to represent the forces acting on the ball as it slows down. (The ball is rolling from left to right)

Direction of movement

The Black Cap batsman hits the next ball 30m into the air.

3.(a) Circle A, B, C or D below to select the sketch that best shows the shape of a speed – time graph of the ball’s motion immediately after it leaves the bat.

Complete worksheet 2for homework

Work

• Work (symbol W) is done when a force moves an object

• If work is done on an object then the object gains energy

• The gain in energy is equal to the work done – so both work and energy are measured in joules (J)

Work

• The amount of work done depends on the size of the force and the distance the object moves

• Therefore work is expressed by:

• Where:

F = the force in newtons which moves the object

d = the distance the object moves in metres

W = work in joules

W=F d

Example

A car is pushed 300 metres by a force of 2000N what was the work done?

W = F x d

= 2000N x 300m

= 600000 J or 600kJ

The work done equals the energy gained by the car ie the car will gain 600kJ of kinetic energy – providing none is lost to friction

Work is done to lift an object.The size of the force needed to lift the object is equal to the weight of the object.

Example 2An object of mass 5kg is lifted 2m off the floor. Calculate the work required to do this.

the weight of the object = m x g = 5 x 10 = 50N

So the force needed to lift the object is 50N

The work done to lift the object is = Fd = 50 x 2 = 100J

The work done equals the gain in energy of the mass. The mass has gained 100J of gravitational potential energy

Complete exercises on sheetremember we can find

W,F or d depending on what we are given

W

F d

X

Use the triangle if you want

Power• Power is the rate at which work is done per second

t

WP

Where:P = power in watts

W = work in joules

T = time in seconds W

P t

X

Question• If a 90kg man climbs some steps with a

vertical height of 15m . How much work did he do?

1. F(weight) = mg = 90kg x 10

= 900N

2. W = F x d = 900N x 15m = 13500 J

Power question• If the man climbed the stairs in 6 seconds

how much power did he use?

1. F(weight) = mg = 90kg x 10

= 900N

2. W = F x d = 900N x 15m = 13500 J

t

WP

6s

13500JP P = 2250W

Starter: Power question• A 200kg girder was raised by a crane 30

metres on to the top of a building in 50 seconds. How much power did the crane use?

1. F(weight) = mg = 200kg x 10

= 2000N

2. W = F x d = 2000N x 30m = 60000 J

t

WP

50s

60000JP P = 1200W

Who is the most Powerful?• In pairs we will work out our power• Measure your mass in kgs• Measure the vertical height of the stairs at the end of A

block. One group do this.• In pairs find the time each person in the pair can run to

the top in seconds• Place at least 5 other results in the table below and

workout the power output of eachName Weight (N) Distance (m) Work (J) Time (s) Power (W)

Mr Macdonald

810N 4.3m 3483J 4.9s 705W

Sophie 480N 4.3 4.1 S 503.5W

Matt 580N 4.3 3.63S 687W

Guy 660N 4.3 3.73s 761W

Yinzhou 700N 4.3 3.16s 953W

Kinetic energy• Every moving object has kinetic energy (Ek )

• The faster an object moves the more kinetic energy it has.

• Increasing mass or speed will increase Ek

Where:

E k = energy in joules

m = mass in kg

v = velocity in ms-1

Ek = ½ mv2Formula

Kinetic Energy Question• A 90kg rider and her 1200kg horse were riding at a

speed of 9 ms-1 how much kinetic energy did they have?

Ek = ½ mv2Formula

= ½ 1290kg x (92) = 645 x 81 = 52245 J

Gravitational Potential Energy (Ep)• When an object is lifted above the earth it gains

gravitational potential energy (Ep)

• The greater the mass or the higher it is lifted the greater the Ep.

Where:

Ep = gravitational potential energy in joules

m = mass in kg

h = distance above the earth in metres (m)

Ep = mghFormula

The Black Cap batsman hits the next ball 30m into the air.

3.(a) Circle A, B, C or D below to select the sketch that best shows the shape of a speed – time graph of the ball’s motion immediately after it leaves the bat.

(b) Calculate the gravitational potential energy of the 0.163 kg ball when it reaches its highest point using the formula EP = m.g.h

(c) Explain how the gravitational potential energy would change if the ball were hit half as high.

• E P = mgh = 0.163kg x 10 x 30m = 48.9 J

(A)

• Hitting the ball half as high means that the ball would only gain half the amount of gravitational potential energy ie

E P = mgh = 0.163kg x 10 x 15m = 24.45 J (A/M)

(d) Explain how the distance–time graph on page 2 would be different if the grass on the field was shorter. (Use the smaller version given here to illustrate your answer if necessary).__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________(M/E)

QUESTION TWO: THE BRICKLAYER

The diagram to the right is of a 60 kg bricklayer who had an accident and fell from a 14 m building after being pulled up by a barrel of bricks on the other end of a single pulley. Use his account of the accident to answer the following questions.

“I tied the rope securely at ground level, then went upstairs and loaded 195kg of bricks into the 5kg barrel (which was 14m high)”

1. Calculate the force of gravity on the barrel and bricks.

________________________________________________________________________________________________________________________________________________________________Weight Force( ) unit (A/M)

“

14 m

Then I went back down, untied the rope and held tightly to ensure a slow descent of the bricks. Imagine my surprise at being jerked off the ground so suddenly! I didn’t think to let go of the rope until my fingers were two knuckles deep into the pulley at the top. At the same time, the barrel hit the ground and the bottom fell out of it”

Calculate the net force that pulled the 60 kg bricklayer into the air.

_____________________________________________________________________________________________________________________________________________________________________________________________________________

_________________________________Force = ( )unit

Discuss the relationship between the gravitational potential energy and the kinetic energy of the bricks as they fell to the ground.

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________A/M

Fiona has just bought her first car using money she has saved from her after school supermarket job. To get to know the car she decides to take a short trip to the beach with her friend Chris.The beach is 3.0 km (3000 m) from her house and it takes her 5 minutes to reach the beach.

(i) How many seconds does it take her to reach the beach?

(ii) Calculate the average speed at which she drives from home to the beach. Give the correct units with your answer.

Evidence Achievement Merit

V = d/t= 3000/300= 10

correct formula chosen

correct answer (unit not needed)

unit m s-1 or m/s unit

Evidence Achievement

5 min 60 s = 300 s 300 s

While Fiona is driving, Chris (a known geek) notes the speed on the speedometer and sketches a graph of the journey. Fiona drives down the road from home and straight on to the beach car park. The graph Chris drew is below.

Evidence Achievement

275 s to 300 s answer

Between what times was Fiona slowing down for the car park.

Speed-time graph of Fiona’s drive

Calculate the maximum acceleration that Fiona reached during the journey.

Speed-time graph of Fiona’s drive

in time change

speedin changea

050

012

a = 0.24 m s–2

The mass of her car is 500 kg.Calculate the unbalanced force acting on the car while she is speeding up at the start of the journey.

in time change

speedin changea

F = ma

= 500 0.24

= 120 N

Evidence Achievement Merit Excellence

=12/50= 0.24 m s–2

F = ma= 500 0.24= 120 N

one formula chosen correctly

Linked answer from part ii) to force equation in part iii)

Both parts completely correct.

= 12/50 = 0.24 m s –2

At the beachFiona carefully moves the car forward into a parking space, taking care to keep well clear of other cars. When she is very close to the right space she turns off the engine and allows the car to come to a stop.(a) On the diagram below draw arrows to show the forces on the car when it is slowing down.

Drag/friction

Weight

Support

Just before Fiona puts the brakes on the car is moving at 2.0 ms-1. It takes her 0.5 s to stop completely. The car has a mass of 500 kg.

(b) Use the formula to calculate the energy of the car before she brakes from 2.0 m s–1.

Give the correct unit with your answer

221

k mvE

Question Evidence Achievement

two (b) = 0.5 500 (2.0)2

= 1000

answer correct

unit J / joule unit

Calculate the net force on the car while it is braking.

Evidence Achievement Merit Excellence

A= v/t= 2.0/0.5= 4.0

F= ma= 500 4.0= 2000 N

one equation correctly selected

answer to either part correctly followed through

Both parts completely correct.

In a second attempt to park, the car must lose 2000 J of energy. The car takes 0.4 m to stop. Calculate the force exerted by the brakes of the car during the braking.Evidence Achievement Merit Excellence

W = F dF = W/d

= 2000/0.4= 5000 N

selection of formula or recognizing work = energy lost

Substitution of energy in correct formula

answer correct + unit

Explain what happened to the energy the car had, during the braking time.

Evidence Achievement Merit

Energy has been converted into heat by the work done as the brakes exert friction on the wheels

Energy lost as heat or lost by friction

Energy lost by heat as a result of friction

In the sunFiona’s parking space is in full sunshine. When she returns to the car to collect her swimming togs, she finds that it is quite hot inside. To cool it down she winds the windows down a little.

(a)She decides that heat has entered through the glass of the closed windows. State the type of heat transfer that happens through clear glass.

Evidence Achievement Merit

radiation correct

Discuss how the colour of a car and slightly open windows could affect the temperature inside the car.

Evidence Achievement Merit Excellence

A light colour would reflect radiation while a darker colour would absorb radiation. The heat could then be conducted to the interior by the metal roof.Open windows would allow rising hot air (convection) to leave the interior to be replaced by cooler air from below. Closed windows would prevent circulation.

one correct statementreflection by lightabsorption by darkconvection when openno circulation when closed.

two statements compared

statements contrasting situations and covering both scenarios.

You will graph your results on the graph paper provided.

Work out the slope of your graph and from this work out your average speed in ms -1

How does your average speed compare with others in the class?

A motorcyclist is traveling at 22m/s for 2 minutes how far did he travel?

m2640

120s x m/s 22

t x v d

You will need the following formula for these starters

V=IR and P=VI

Ohms law starter Question

If 4 amps of current are flowing through a light connected to a 12 V supply what is the resistance of the lamp?

V = I x R to get R = V/I

R = 12 V/4 A = 3

If a resistor has a resistance of 6 and a voltmeter reads 24 volts in the circuit how much current is flowing in the circuit?

V =IR

I = V/R

I = 24V/6 = 4A

A Hitachi power drill plugged into a socket uses 800 watts of energy. What current does it draw?

A333.3240V

W800

V

P I

VI P

A fuse is designed to break if the current gets too large

Why is fuse placed in a circuit?

What is a watt ?

The watt is the unit for power. One watt is a joule of energy used or supplied per second

Use the following circuit to answer the questions

A3

A2

A4

A1

V 1. If each of the cells is rated at 2.5 volts what would the voltmeter read?2.5v + 2.5v + 2.5v = 7.5v

(A)

2. If each lamp had a resistance of 1.25 ohms calculate the total resistance in the circuit

1.25 + 1.25 + 1.25 = 3.75 (A)

2A Ω 3.75

V 7.5 I

R

V I R I V usingcurrent t 1st workou

3. How much power would the circuit use? (M/E)

(W) watts14 2A x V 7.5 P

VIP usingpower workout Now

in time change

citystart velo - velocity final a

A motorbike travelling from Dunedin to Christchurch adjusts his speed taking 5 seconds to go from 55ms-1 to 10ms-1. What is his acceleration?

2-

1-

-1-1

ms15 a

seconds 3

45ms -

seconds 3

55ms - 10ms

a

a

Remember negative acceleration is decceleration