ConcepTest 6.1aConcepTest 6.1a Tension ITension I

1) 0 N

2) 50 N

3) 100 N

4) 150 N

5) 200 N

You tie a rope to a tree and you

pull on the rope with a force of

100 N. What is the tension in

the rope?

The tension in the rope is the force that the rope “feels”

across any section of it (or that you would feel if you

replaced a piece of the rope). Since you are pulling with

a force of 100 N, that is the tension in the rope.

ConcepTest 6.1aConcepTest 6.1a Tension ITension I

1) 0 N

2) 50 N

3) 100 N

4) 150 N

5) 200 N

You tie a rope to a tree and you

pull on the rope with a force of

100 N. What is the tension in

the rope?

1) 0 N

2) 50 N

3) 100 N

4) 150 N

5) 200 N

Two tug-of-war opponents each

pull with a force of 100 N on

opposite ends of a rope. What

is the tension in the rope?

ConcepTest 6.1bConcepTest 6.1b Tension IITension II

This is literallyliterally the identical situation to the previous

question. The tension is not 200 N !!The tension is not 200 N !! Whether the other

end of the rope is pulled by a person, or pulled by a tree,

the tension in the rope is still 100 N100 N !!

1) 0 N

2) 50 N

3) 100 N

4) 150 N

5) 200 N

Two tug-of-war opponents each

pull with a force of 100 N on

opposite ends of a rope. What

is the tension in the rope?

ConcepTest 6.1bConcepTest 6.1b Tension IITension II

1) you and your friend each pull on opposite ends of the rope

2) tie the rope to a tree, and you both pull from the same end

3) it doesn’t matter -- both of the above are equivalent

4) get a large dog to bite the rope

You and a friend can

each pull with a force of

20 N. If you want to rip

a rope in half, what is

the best way?

ConcepTest 6.1cConcepTest 6.1c Tension IIITension III

Take advantage of the fact that the tree can pull with

almost any force (until it falls down, that is!). You

and your friend should team up on one end, and let

the tree make the effort on the other end.

1) you and your friend each pull on opposite ends of the rope

2) tie the rope to a tree, and you both pull from the same end

3) it doesn’t matter -- both of the above are equivalent

4) get a large dog to bite the rope

You and a friend can

each pull with a force of

20 N. If you want to rip

a rope in half, what is

the best way?

ConcepTest 6.1cConcepTest 6.1c Tension IIITension III

ConcepTest 6.2 ConcepTest 6.2 Three BlocksThree Blocks

T3 T2 T13m 2m m

a

1) T1 > T2 > T3

2) T1 < T2 < T3

3) T1 = T2 = T3

4) all tensions are zero

5) tensions are random

Three blocks of mass 3m, 2m, and

m are connected by strings and

pulled with constant acceleration a.

What is the relationship between

the tension in each of the strings?

TT11 pulls the wholewhole setset of

blocks along, so it must be

the largestlargest. T2 pulls the last

two masses, but T3 only pulls

the last mass.

ConcepTest 6.2 ConcepTest 6.2 Three BlocksThree Blocks

T3 T2 T13m 2m m

a

1) T1 > T2 > T3

2) T1 < T2 < T3

3) T1 = T2 = T3

4) all tensions are zero

5) tensions are random

Three blocks of mass 3m, 2m, and

m are connected by strings and

pulled with constant acceleration a.

What is the relationship between

the tension in each of the strings?

Follow-up:Follow-up: What is What is TT11 in terms of in terms of mm and and aa??

ConcepTest 6.3ConcepTest 6.3 Over the EdgeOver the Edge

m

10kg a

m

a

F = 98 N

Case (1) Case (2)

1) case 1

2) acceleration is zero

3) both cases are the same

4) depends on value of m

5) case 2

In which case does block m experience

a larger acceleration? In (1) there is a

10 kg mass hanging from a rope and

falling. In (2) a hand is providing a

constant downward force of 98 N.

Assume massless ropes.

In (2) the tension is 98 N

due to the hand. In (1)

the tension is lessless than

98 N because the block

is accelerating downaccelerating down.

Only if the block were at

rest would the tension

be equal to 98 N.

ConcepTest 6.3ConcepTest 6.3 Over the EdgeOver the Edge

m

10kg a

m

a

F = 98 N

Case (1) Case (2)

1) case 1

2) acceleration is zero

3) both cases are the same

4) depends on value of m

5) case 2

In which case does block m experience

a larger acceleration? In (1) there is a

10 kg mass hanging from a rope and

falling. In (2) a hand is providing a

constant downward force of 98 N.

Assume massless ropes.

ConcepTest 6.4ConcepTest 6.4 FrictionFriction

1) the force from the rushing air pushed

it off

2) the force of friction pushed it off

3) no net force acted on the box

4) truck went into reverse by accident

5) none of the above

A box sits in a pickup truck

on a frictionless truck bed.

When the truck accelerates

forward, the box slides off

the back of the truck

because:

Generally, the reason that the box in the truck bed would move

with the truck is due to frictionfriction between the box and the bed.

If there is no friction, there is no force to push the box along, If there is no friction, there is no force to push the box along,

and it remains at rest.and it remains at rest. The truck accelerated away, essentially

leaving the box behind!!

ConcepTest 6.4ConcepTest 6.4 FrictionFriction

1) the force from the rushing air pushed

it off

2) the force of friction pushed it off

3) no net force acted on the box

4) truck went into reverse by accident

5) none of the above

A box sits in a pickup truck

on a frictionless truck bed.

When the truck accelerates

forward, the box slides off

the back of the truck

because:

Antilock brakes keep the

car wheels from locking

and skidding during a

sudden stop. Why does

this help slow the car

down?

1) k > s so sliding friction is better

2) k > s so static friction is better

3) s > k so sliding friction is better

4) s > k so static friction is better

5) none of the above

ConcepTest 6.5ConcepTest 6.5 Antilock BrakesAntilock Brakes

Antilock brakes keep the

car wheels from locking

and skidding during a

sudden stop. Why does

this help slow the car

down?

1) k > s so sliding friction is better

2) k > s so static friction is better

3) s > k so sliding friction is better

4) s > k so static friction is better

5) none of the above

Static friction is greater than sliding frictionStatic friction is greater than sliding friction, so

by keeping the wheels from skidding, the static

friction force will help slow the car down more

efficiently than the sliding friction that occurs

during a skid.

ConcepTest 6.5ConcepTest 6.5 Antilock BrakesAntilock Brakes

ConcepTest 6.6ConcepTest 6.6 Going SleddingGoing Sledding

1

2

1) pushing her from behind

2) pulling her from the front

3) both are equivalent

4) it is impossible to move the sled

5) tell her to get out and walk

Your little sister wants

you to give her a ride

on her sled. On level

ground, what is the

easiest way to

accomplish this?

ConcepTest 6.6ConcepTest 6.6 Going SleddingGoing Sledding

1

2

In Case 1, the force F is pushing downpushing down

(in addition to mg), so the normal normal

force is largerforce is larger. In Case 2, the force F

is pulling uppulling up, against gravity, so the

normal force is lessenednormal force is lessened. Recall that

the frictional force is proportional to

the normal force.

1) pushing her from behind

2) pulling her from the front

3) both are equivalent

4) it is impossible to move the sled

5) tell her to get out and walk

Your little sister wants

you to give her a ride

on her sled. On level

ground, what is the

easiest way to

accomplish this?

ConcepTest 6.7ConcepTest 6.7 Will it Budge?Will it Budge?

1) moves to the left

2) moves to the right

3) moves up

4) moves down

5) the box does not move

A box of weight 100 N is at

rest on a floor where s = 0.5.

A rope is attached to the box

and pulled horizontally with

tension T = 30 N. Which way

does the box move?

Tm

Static friction

(s= 0.4)

The static friction force has a

maximummaximum of ssN = 40 NN = 40 N. The

tension in the rope is only 30 N30 N.

So the pulling force is not big

enough to overcome friction.

ConcepTest 6.7ConcepTest 6.7 Will it Budge?Will it Budge?

1) moves to the left

2) moves to the right

3) moves up

4) moves down

5) the box does not move

A box of weight 100 N is at

rest on a floor where s = 0.5.

A rope is attached to the box

and pulled horizontally with

tension T = 30 N. Which way

does the box move?

Tm

Static friction

(s= 0.4)

Follow-up:Follow-up: What happens if the tension is What happens if the tension is 35 N35 N? What about ? What about 45 N45 N??

1) component of the gravity force parallel to the plane increased

2) coeff. of static friction decreased

3) normal force exerted by the board decreased

4) both #1 and #3

5) all of #1, #2 and #3

A box sits on a flat board.

You lift one end of the

board, making an angle

with the floor. As you

increase the angle, the

box will eventually begin

to slide down. Why?

Net Force

Normal

Weight

ConcepTest 6.8aConcepTest 6.8a Sliding Down ISliding Down I

1) component of the gravity force parallel to the plane increased

2) coeff. of static friction decreased

3) normal force exerted by the board decreased

4) both #1 and #3

5) all of #1, #2 and #3

A box sits on a flat board.

You lift one end of the

board, making an angle

with the floor. As you

increase the angle, the

box will eventually begin

to slide down. Why?

Net Force

Normal

Weight

As the angle increases, the component of component of

weight parallel to the plane increasesweight parallel to the plane increases and

the component perpendicular to the plane component perpendicular to the plane

decreasesdecreases (and so does the Normal force).

Since friction depends on Normal force, we

see that the friction force gets smallerfriction force gets smaller and

the force pulling the box down the plane force pulling the box down the plane

gets biggergets bigger.

ConcepTest 6.8aConcepTest 6.8a Sliding Down ISliding Down I

m

1) not move at all

2) slide a bit, slow down, then stop

3) accelerate down the incline

4) slide down at constant speed

5) slide up at constant speed

A mass m is placed on an

inclined plane ( > 0) and

slides down the plane with

constant speed. If a similar

block (same ) of mass 2m

were placed on the same

incline, it would:

ConcepTest 6.8bConcepTest 6.8b Sliding Down IISliding Down II

The component of gravity acting down

the plane is doubledouble for 2m. However,

the normal force (and hence the friction

force) is also doubledouble (the same factor!).

This means the two forces still cancel

to give a net force of zero.

A mass m is placed on an

inclined plane ( > 0) and

slides down the plane with

constant speed. If a similar

block (same ) of mass 2m

were placed on the same

incline, it would:

W

Nf

Wx

Wy

1) not move at all

2) slide a bit, slow down, then stop

3) accelerate down the incline

4) slide down at constant speed

5) slide up at constant speed

ConcepTest 6.8bConcepTest 6.8b Sliding Down IISliding Down II

ConcepTest 6.9ConcepTest 6.9 TetherballTetherball1) Toward the top of the poleToward the top of the pole

2) Toward the groundToward the ground

3) Along the horizontal component of Along the horizontal component of the tension forcethe tension force

4) Along the vertical component of the Along the vertical component of the tension forcetension force

5) Tangential to the circleTangential to the circle

In the game of tetherball, In the game of tetherball,

the struck ball whirls the struck ball whirls

around a pole. In what around a pole. In what

direction does the direction does the net net

forceforce on the ball point? on the ball point?

W

T

The vertical component of the vertical component of the

tensiontension balances the weightweight. The

horizontal component of tensionhorizontal component of tension

provides the centripetal forcecentripetal force that

points toward the center of the

circle.

1) Toward the top of the poleToward the top of the pole

2) Toward the groundToward the ground

3) Along the horizontal component of Along the horizontal component of the tension forcethe tension force

4) Along the vertical component of the Along the vertical component of the tension forcetension force

5) Tangential to the circleTangential to the circle

In the game of tetherball, In the game of tetherball,

the struck ball whirls the struck ball whirls

around a pole. In what around a pole. In what

direction does the direction does the net net

forceforce on the ball point? on the ball point?

W T

W

T

ConcepTest 6.9ConcepTest 6.9 TetherballTetherball

You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective in the car, what do you feel is happening to you?

(1) You are thrown to the right

(2) You feel no particular change

(3) You are thrown to the left

(4) You are thrown to the ceiling

(5) You are thrown to the floor

ConcepTest 6.10aConcepTest 6.10a Around the Curve IAround the Curve I

You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective in the car, what do you feel is happening to you?

(1) You are thrown to the right

(2) You feel no particular change

(3) You are thrown to the left

(4) You are thrown to the ceiling

(5) You are thrown to the floor

ConcepTest 6.10aConcepTest 6.10a Around the Curve IAround the Curve I

The passenger has the tendency to

continue moving in a straight line. From

your perspective in the car, it feels like

you are being thrown to the right, hitting

the passenger door.

(1) centrifugal force is pushing you into the door

(2) the door is exerting a leftward force on you

(3) both of the above

(4) neither of the above

During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening?

ConcepTest 6.10bConcepTest 6.10b Around the Curve IIAround the Curve II

(1) centrifugal force is pushing you into the door

(2) the door is exerting a leftward force on you

(3) both of the above

(4) neither of the above

During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening?

The passenger has the tendency to

continue moving in a straight line. There

is a centripetal force, provided by the

door, that forces the passenger into a

circular path.

ConcepTest 6.10bConcepTest 6.10b Around the Curve IIAround the Curve II

(1) car’s engine is not strong enough to (1) car’s engine is not strong enough to keep the car from being pushed outkeep the car from being pushed out

(2) friction between tires and road is not (2) friction between tires and road is not strong enough to keep car in a circlestrong enough to keep car in a circle

(3) car is too heavy to make the turn(3) car is too heavy to make the turn

(4) a deer caused you to skid(4) a deer caused you to skid

(5) none of the above(5) none of the above

You drive your dad’s car You drive your dad’s car too fast around a curve too fast around a curve and the car starts to skid. and the car starts to skid. What is the correct What is the correct description of this description of this situation?situation?

ConcepTest 6.10cConcepTest 6.10c Around the Curve IIIAround the Curve III

The friction force between tires and

road provides the centripetal force

that keeps the car moving in a circle.

If this force is too small, the car

continues in a straight line!

(1) car’s engine is not strong enough to (1) car’s engine is not strong enough to keep the car from being pushed outkeep the car from being pushed out

(2) friction between tires and road is not (2) friction between tires and road is not strong enough to keep car in a circlestrong enough to keep car in a circle

(3) car is too heavy to make the turn(3) car is too heavy to make the turn

(4) a deer caused you to skid(4) a deer caused you to skid

(5) none of the above(5) none of the above

You drive your dad’s car You drive your dad’s car too fast around a curve too fast around a curve and the car starts to skid. and the car starts to skid. What is the correct What is the correct description of this description of this situation?situation?

ConcepTest 6.10cConcepTest 6.10c Around the Curve IIIAround the Curve III

Follow-up:Follow-up: What could be done to What could be done to the road or car to prevent skidding?the road or car to prevent skidding?

ConcepTest 6.11ConcepTest 6.11 Missing LinkMissing Link

A ping pong ball is shot into a

circular tube that is lying flat

(horizontal) on a tabletop. When

the ping pong ball leaves the

track, which path will it follow?

ConcepTest 6.11ConcepTest 6.11 Missing LinkMissing Link

Once the ball leaves the tube, there is no longer

a force to keep it going in a circle. Therefore, it

simply continues in a straight line, as Newton’s

First Law requires!

A ping pong ball is shot into a

circular tube that is lying flat

(horizontal) on a tabletop. When

the ping pong ball leaves the

track, which path will it follow?

Follow-up:Follow-up: What physical force provides the centripetal force? What physical force provides the centripetal force?

ConcepTest 6.12ConcepTest 6.12 Ball and StringBall and String

1) T2 = 1/4 T1

2) T2 = 1/2 T1

3) T2 = T1

4) T2 = 2 T1

5) T2 = 4 T1

Two equal-mass rocks tied to strings are Two equal-mass rocks tied to strings are

whirled in horizontal circles. The whirled in horizontal circles. The radiusradius of of

circle 2 is circle 2 is twicetwice that of circle 1. If the that of circle 1. If the periodperiod

of motion is the of motion is the samesame for both rocks, for both rocks, what what

is the tension in cord 2 compared to cord 1is the tension in cord 2 compared to cord 1??

The centripetal force in this case is given by the tension,

so TT = = mvmv22//rr. For the same period, we find that vv22 = 2 = 2vv11

(and this term is squared). However, for the denominator,

we see that rr22 = 2 = 2rr11 which gives us the relation TT22 = 2 = 2TT11.

ConcepTest 6.12ConcepTest 6.12 Ball and StringBall and String

Two equal-mass rocks tied to strings are Two equal-mass rocks tied to strings are

whirled in horizontal circles. The whirled in horizontal circles. The radiusradius of of

circle 2 is circle 2 is twicetwice that of circle 1. If the that of circle 1. If the periodperiod

of motion is the of motion is the samesame for both rocks, for both rocks, what what

is the tension in cord 2 compared to cord 1is the tension in cord 2 compared to cord 1??

1) T2 = 1/4 T1

2) T2 = 1/2 T1

3) T2 = T1

4) T2 = 2 T1

5) T2 = 4 T1

ConcepTest 6.13ConcepTest 6.13 Barrel of FunBarrel of Fun

A rider in a “barrel of fun” A rider in a “barrel of fun”

finds herself stuck with finds herself stuck with

her back to the wall. her back to the wall.

Which diagram correctly Which diagram correctly

shows the forces acting shows the forces acting

on her?on her?1 2 3 4 5

The normal forcenormal force of the wall on the

rider provides the centripetal forcecentripetal force

needed to keep her going around

in a circle. The downward force of downward force of

gravity is balanced by the upward gravity is balanced by the upward

frictional forcefrictional force on her, so she does

not slip vertically.

ConcepTest 6.13ConcepTest 6.13 Barrel of FunBarrel of Fun

A rider in a “barrel of fun” A rider in a “barrel of fun”

finds herself stuck with finds herself stuck with

her back to the wall. her back to the wall.

Which diagram correctly Which diagram correctly

shows the forces acting shows the forces acting

on her?on her?1 2 3 4 5

Follow-up:Follow-up: What happens if the rotation of the ride slows down? What happens if the rotation of the ride slows down?

ConcepTest 6.14aConcepTest 6.14a Going in Circles IGoing in Circles I

1) 1) NN remains equal to remains equal to mgmg

2) 2) NN is smaller than is smaller than mgmg

3) 3) NN is larger than is larger than mgmg

4) None of the above4) None of the above

You’re on a Ferris wheel moving in a You’re on a Ferris wheel moving in a

vertical circle. When the Ferris wheel is vertical circle. When the Ferris wheel is

at rest, the at rest, the normal force normal force NN exerted by exerted by

your seat is equal to your your seat is equal to your weight weight mgmg. .

How does How does NN change at the top of the change at the top of the

Ferris wheel when you are in motion?Ferris wheel when you are in motion?

ConcepTest 6.14aConcepTest 6.14a Going in Circles IGoing in Circles I

1) 1) NN remains equal to remains equal to mgmg

2) 2) NN is smaller than is smaller than mgmg

3) 3) NN is larger than is larger than mgmg

4) None of the above4) None of the above

You’re on a Ferris wheel moving in a You’re on a Ferris wheel moving in a

vertical circle. When the Ferris wheel is vertical circle. When the Ferris wheel is

at rest, the at rest, the normal force normal force NN exerted by exerted by

your seat is equal to your your seat is equal to your weight weight mgmg. .

How does How does NN change at the top of the change at the top of the

Ferris wheel when you are in motion?Ferris wheel when you are in motion?

You are in circular motion, so there has to

be a centripetal force pointing inwardinward. At

the top, the only two forces are mgmg (down) (down)

and NN (up) (up), so NN must be smaller than must be smaller than mgmg.

Follow-up:Follow-up: Where is Where is NN larger than larger than mgmg??

R

vv

1) 1) FFcc = = NN + + mgmg

2) 2) FFcc = = mgmg – – NN

3) 3) FFcc = = TT + + NN – – mgmg

4) 4) FFcc = = NN

5) 5) FFcc = = mgmg

A skier goes over a small round hill A skier goes over a small round hill

with radius with radius RR. Since she is in circular . Since she is in circular

motion, there has to be a motion, there has to be a centripetal centripetal

force.force. At the top of the hill, what is At the top of the hill, what is

FFcc of the skier equal to? of the skier equal to?

ConcepTest 6.14bConcepTest 6.14b Going in Circles IIGoing in Circles II

R

vvFFcc points toward the center of the points toward the center of the

circle, circle, i.ei.e., downward in this case.., downward in this case. The weight vectorweight vector points downdown and the normal forcenormal force (exerted by the hill) points upup. The magnitude of the net

force, therefore, is: FFcc = = mgmg – – NN

mgg NN

A skier goes over a small round hill A skier goes over a small round hill

with radius R. Since she is in circular with radius R. Since she is in circular

motion, there has to be a motion, there has to be a centripetal centripetal

force.force. At the top of the hill, what is At the top of the hill, what is

FFcc of the skier equal to? of the skier equal to?

ConcepTest 6.14bConcepTest 6.14b Going in Circles IIGoing in Circles II

Follow-up:Follow-up: What happens when What happens when the skier goes into a small dip?the skier goes into a small dip?

1) 1) FFcc = = NN + + mgmg

2) 2) FFcc = = mgmg – – NN

3) 3) FFcc = = TT + + NN – – mgmg

4) 4) FFcc = = NN

5) 5) FFcc = = mgmg

R

vtop

1) 1) FFcc = = TT – – mgmg

2) 2) FFcc = = TT + + NN – – mgmg

3) 3) FFcc = = TT + + mgmg

4) 4) FFcc = = T T

5) 5) FFcc = = mgmg

ConcepTest 6.15cConcepTest 6.15c Going in Circles IIIGoing in Circles III

You swing a ball at the end of string You swing a ball at the end of string

in a vertical circle. Since the ball is in a vertical circle. Since the ball is

in circular motion there has to be a in circular motion there has to be a

centripetal force.centripetal force. At the top of the At the top of the

ball’s path, what is ball’s path, what is FFcc equal to? equal to?

R

vTTmgg

You swing a ball at the end of string You swing a ball at the end of string

in a vertical circle. Since the ball is in a vertical circle. Since the ball is

in circular motion there has to be a in circular motion there has to be a

centripetal force.centripetal force. At the top of the At the top of the

ball’s path, what is ball’s path, what is FFcc equal to? equal to?

FFcc points toward the center of the circle, points toward the center of the circle,

i.ei.e. downward in this case.. downward in this case. The weight weight

vectorvector points downdown and the tensiontension

(exerted by the string) also points downdown.

The magnitude of the net force, therefore,

is: FFcc = = TT + + mgmg

ConcepTest 6.15cConcepTest 6.15c Going in Circles IIIGoing in Circles III

Follow-up:Follow-up: What is What is FFcc at the bottom of the ball’s path? at the bottom of the ball’s path?

1) 1) FFcc = = TT – – mgmg

2) 2) FFcc = = TT + + NN – – mgmg

3) 3) FFcc = = TT + + mgmg

4) 4) FFcc = = T T

5) 5) FFcc = = mgmg