Physics Semester I

Physics Semester I Final Review

If each component of a

vector is doubled, what

happens to the angle of

that vector?

1) it doubles2) it increases, but by less than double3) it does not change 4) it is reduced by half5) it decreases, but not as much as half

ConcepTest 3.2a Vector Components I

If each component of a

vector is doubled, what

happens to the angle of

that vector?

1) it doubles2) it increases, but by less than double3) it does not change 4) it is reduced by half5) it decreases, but not as much as half

The magnitude of the vector clearly doubles if each of its components is doubled. But the angle of the vector is given by tan q = 2y/2x, which is the same as tan q = y/x (the original angle).

Follow-up: If you double one component and not the other, how would the angle change?

ConcepTest 3.2a Vector Components I

ConcepTest 3.4a Firing Balls I

A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball?

1) it depends on how fast the cart is moving

2) it falls behind the cart3) it falls in front of the cart4) it falls right back into the cart5) it remains at rest

ConcepTest 3.4a Firing Balls IA small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball?

1) it depends on how fast the cart is moving

2) it falls behind the cart3) it falls in front of the cart4) it falls right back into the cart5) it remains at rest

when viewed from

train

when viewed from

ground

In the frame of reference of the cart, the ball only has a vertical component of velocity. So it goes up and comes back down. To a ground observer, both the cart and the ball have the same horizontal velocity, so the ball still returns into the cart.

Now the cart is being pulled along a horizontal track by an external force (a weight hanging over the table edge) and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball?

1) it depends upon how much the track is tilted2) it falls behind the cart3) it falls in front of the cart4) it falls right back into the cart5) it remains at rest

ConcepTest 3.4b Firing Balls II

Now the cart is being pulled along a horizontal track by an external force (a weight hanging over the table edge) and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball?


Now the acceleration of the cart is completely unrelated to the ball. In fact, the ball does not have any horizontal acceleration at all (just like the first question), so it will lag behind the accelerating cart once it is shot out of the cannon.

ConcepTest 3.4b Firing Balls II

The same small cart is now rolling down an inclined track and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball?


ConcepTest 3.4c Firing Balls III

The same small cart is now rolling down an inclined track and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball?


Because the track is inclined, the cart accelerates. However, the ball has the same component of acceleration along the track as the cart does! This is essentially the component of g acting parallel to the inclined track. So the ball is effectively accelerating down the incline, just as the cart is, and it falls back into the cart.

ConcepTest 3.4c Firing Balls III

ConcepTest 3.5 Dropping a PackageYou drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will:

1) quickly lag behind the plane while falling

2) remain vertically under the plane while falling

3) move ahead of the plane while falling

4) not fall at all

You drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will:

1) quickly lag behind the plane while falling

2) remain vertically under the plane while falling

3) move ahead of the plane while falling

4) not fall at all

Both the plane and the package have

the same horizontal velocity at the

moment of release. They will

maintain this velocity in the x-

direction, so they stay aligned.

Follow-up: What would happen if air resistance were present?

ConcepTest 3.5 Dropping a Package

ConcepTest 3.6a Dropping the Ball I

From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first?

1) the “dropped” ball2) the “fired” ball3) they both hit at the same time4) it depends on how hard the ball

was fired5) it depends on the initial height

From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first?

1) the “dropped” ball2) the “fired” ball3) they both hit at the same time4) it depends on how hard the ball

was fired5) it depends on the initial height

Both of the balls are falling vertically under the influence of

gravity. They both fall from the same height. Therefore, they will

hit the ground at the same time. The fact that one is moving

horizontally is irrelevant – remember that the x and y motions are

completely independent !!

Follow-up: Is that also true if there is air resistance?

ConcepTest 3.6a Dropping the Ball I

ConcepTest 3.6b Dropping the Ball II

In the previous

problem, which ball

has the greater velocity

at ground level?

1) the “dropped” ball2) the “fired” ball3) neither – they both have the

same velocity on impact4) it depends on how hard the

ball was thrown

In the previous problem,

which ball has the

greater velocity at

ground level?

1) the “dropped” ball2) the “fired” ball3) neither – they both have the

same velocity on impact4) it depends on how hard the

ball was thrown

Both balls have the same vertical velocity when they hit the ground (since they are both acted on by gravity for the same time). However, the “fired” ball also has a horizontal velocity. When you add the two components vectorially, the “fired” ball has a larger net velocity when it hits the ground.

Follow-up: What would you have to do to have them both reach the same final velocity at ground level?

ConcepTest 3.6b Dropping the Ball II

ConcepTest 3.6c Dropping the Ball III

A projectile is launched from the ground at an angle of 30o. At what point in its trajectory does this projectile have the least speed?

1) just after it is launched2) at the highest point in its flight3) just before it hits the ground4) halfway between the ground and

the highest point 5) speed is always constant

A projectile is launched from the ground at an angle of 30o. At what point in its trajectory does this projectile have the least speed?

1) just after it is launched2) at the highest point in its flight3) just before it hits the ground4) halfway between the ground and

the highest point 5) speed is always constant

The speed is smallest at

the highest point of its

flight path because the y-

component of the velocity

is zero.

ConcepTest 3.6c Dropping the Ball III

ConcepTest 4.1a Newton’s First Law I1) there is a net force but the book has too

much inertia2) there are no forces acting on it at all3) it does move, but too slowly to be seen4) there is no net force on the book5) there is a net force, but the book is too

heavy to move

A book is lying at rest on a table. The book will remain there at rest because:

There are forces acting on the book, but the only

forces acting are in the y-direction. Gravity acts

downward, but the table exerts an upward force

that is equally strong, so the two forces cancel,

leaving no net force.

ConcepTest 4.1a Newton’s First Law I1) there is a net force but the book has too

much inertia2) there are no forces acting on it at all3) it does move, but too slowly to be seen4) there is no net force on the book5) there is a net force, but the book is too

heavy to move

A book is lying at rest on a table. The book will remain there at rest because:

ConcepTest 4.1b Newton’s First Law II

1) more than its weight2) equal to its weight3) less than its weight but more than zero4) depends on the speed of the puck5) zero

A hockey puck slides on ice at constant velocity. What is the net force acting on the puck?

The puck is moving at a constant velocity, and

therefore it is not accelerating. Thus, there must

be no net force acting on the puck.

ConcepTest 4.1b Newton’s First Law II

1) more than its weight2) equal to its weight3) less than its weight but more than zero4) depends on the speed of the puck5) zero

A hockey puck slides on ice at constant velocity. What is the net force acting on the puck?

Follow-up: Are there any forces acting on the puck? What are they?

ConcepTest 4.7a Gravity and Weight I

1) Fg is greater on the feather

2) Fg is greater on the stone

3) Fg is zero on both due to vacuum

4) Fg is equal on both always

5) Fg is zero on both always

What can you

say about the

force of

gravity Fg

acting on a

stone and a

feather?

The force of gravity (weight) depends on the mass of the object!! The stone has more mass, therefore more weight.

ConcepTest 4.7a Gravity and Weight I

1) Fg is greater on the feather

2) Fg is greater on the stone

3) Fg is zero on both due to vacuum

4) Fg is equal on both always

5) Fg is zero on both always

What can you say

about the force of

gravity Fg acting

on a stone and a

feather?

1) it is greater on the feather2) it is greater on the stone3) it is zero on both due to vacuum4) it is equal on both always5) it is zero on both always

What can you

say about the

acceleration of

gravity acting

on the stone

and the

feather?

ConcepTest 4.7b Gravity and Weight II

The acceleration is given by F/m so here the mass divides out. Since we know that the force of gravity (weight) is mg, then we end up with acceleration g for both objects.

1) it is greater on the feather2) it is greater on the stone3) it is zero on both due to vacuum4) it is equal on both always5) it is zero on both always

What can you say

about the acceleration

of gravity acting on

the stone and the

feather?

ConcepTest 4.7b Gravity and Weight II

Follow-up: Which one hits the bottom first?

ConcepTest 4.9a Going Up IA block of mass m rests on the floor of an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block?

1) N > mg2) N = mg3) N < mg (but not zero)4) N = 0 5) depends on the size of the

elevator

m

v

The block is moving at constant speed, so

it must have no net force on it. The forces

on it are N (up) and mg (down), so N = mg,

just like the block at rest on a table.

ConcepTest 4.9a Going Up IA block of mass m rests on the floor of an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block?


elevator

m

v

A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block?


elevator

ConcepTest 4.9b Going Up II

m

a

The block is accelerating upward, so

it must have a net upward force. The

forces on it are N (up) and mg (down),

so N must be greater than mg in order

to give the net upward force!


elevator

S F = N – mg = ma > 0 \ N > mg

m a > 0

mg

N

A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block?

ConcepTest 4.9b Going Up II

Follow-up: What is the normal force if the elevator is in free fall downward?

ConcepTest 4.10 Normal Force

Case 1

Case 2

Below you see two cases: a physics student pulling or pushing a sled with a force F which is applied at an angle q. In which case is the normal force greater?

1) case 12) case 23) it’s the same for both4) depends on the magnitude of

the force F5) depends on the ice surface

In Case 1, the force F is pushing down

(in addition to mg), so the normal force

needs to be larger. In Case 2, the force F

is pulling up, against gravity, so the

normal force is lessened.

ConcepTest 4.10 Normal Force

Case 1

Case 2

Below you see two cases: a physics student pulling or pushing a sled with a force F which is applied at an angle q. In which case is the normal force greater?

1) case 12) case 23) it’s the same for both4) depends on the magnitude of

the force F5) depends on the ice surface

ConcepTest 4.11 On an Incline1) case A2) case B3) both the same (N = mg)4) both the same (0 < N < mg)5) both the same (N = 0)

Consider two identical blocks, one resting on a flat surface and the other resting on an incline. For which case is the normal force greater?

1) case A2) case B3) both the same (N = mg)4) both the same (0 < N < mg)5) both the same (N = 0)

N

WWy

x

y

f

q

q

ConcepTest 4.11 On an InclineConsider two identical blocks, one resting on a flat surface and the other resting on an incline. For which case is the normal force greater?

In Case A, we know that N = W.

In Case B, due to the angle of

the incline, N < W. In fact, we

can see that N = W cos(q).

ConcepTest 4.12 Climbing the Rope

When you climb up a

rope, the first thing

you do is pull down

on the rope. How do

you manage to go up

the rope by doing

that??

1) this slows your initial velocity, which is already upward

2) you don’t go up, you’re too heavy3) you’re not really pulling down – it

just seems that way4) the rope actually pulls you up5) you are pulling the ceiling down

When you pull down on the rope, the rope pulls up on

you!! It is actually this upward force by the rope that

makes you move up! This is the “reaction” force (by the

rope on you) to the force that you exerted on the rope.

And voilá, this is Newton’s Third Law.

ConcepTest 4.12 Climbing the RopeWhen you climb up a

rope, the first thing you

do is pull down on the

rope. How do you

manage to go up the

rope by doing that??

1) this slows your initial velocity, which is already upward

2) you don’t go up, you’re too heavy3) you’re not really pulling down – it

just seems that way4) the rope actually pulls you up5) you are pulling the ceiling down

ConcepTest 4.14a Collision Course I

A small car collides with a large truck. Which experiences the greater impact force?

1) the car2) the truck3) both the same4) it depends on the velocity of each5) it depends on the mass of each

ConcepTest 4.14a Collision Course I

A small car collides with a large truck. Which experiences the greater impact force?


According to Newton’s Third Law, both vehicles

experience the same magnitude of force.


In the collision between the car and the truck, which has the greater acceleration?

ConcepTest 4.14b Collision Course II


In the collision between the car and the truck, which has the greater acceleration?

ConcepTest 4.14b Collision Course II

We have seen that both vehicles experience the same magnitude of force. But the acceleration is given by F/m so the car has the larger acceleration, since it has the smaller mass.

ConcepTest 4.21 Going Sledding

1

2

1) pushing her from behind2) pulling her from the front3) both are equivalent4) it is impossible to move the sled5) 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 4.21 Going Sledding

1

2

In Case 1, the force F is pushing down (in addition to mg), so the normal force is larger. In Case 2, the force F is pulling up, against gravity, so the normal force is lessened. Recall that the frictional force is proportional to the normal force.

1) pushing her from behind2) pulling her from the front3) both are equivalent4) it is impossible to move the sled5) 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 4.22 Will it Budge?

1) moves to the left2) moves to the right3) moves up4) moves down5) the box does not move

A box of weight 100 N is at rest on a floor where ms = 0.5. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move?

TmStatic friction

(ms = 0.4 )

The static friction force has a maximum of msN = 40 N. The

tension in the rope is only 30 N. So the pulling force is not big enough to overcome friction.

ConcepTest 4.22 Will it Budge?1) moves to the left2) moves to the right3) moves up4) moves down5) the box does not move

A box of weight 100 N is at rest on a floor where ms = 0.5. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move?

TmStatic friction

(ms = 0.4 )

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

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

2) coeff. of static friction decreased3) normal force exerted by the board

decreased4) both #1 and #35) 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 4.23a Sliding Down I

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

2) coeff. of static friction decreased3) normal force exerted by the board

decreased4) both #1 and #35) 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 weight parallel to the plane increases and the component perpendicular to the plane decreases (and so does the normal force). Since friction depends on normal force, we see that the friction force gets smaller and the force pulling the box down the plane gets bigger.

ConcepTest 4.23a Sliding Down I

Is it possible to do work on an

object that remains at rest? 1) yes

2) no

ConcepTest 5.1 To Work or Not to Work

Is it possible to do work on an

object that remains at rest? 1) yes

2) no

Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done.

ConcepTest 5.1 To Work or Not to Work

ConcepTest 5.2a Friction and Work I

1) friction does no work at all

2) friction does negative work

3) friction does positive work

A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?

f

N

mg

displacement

Pull

Friction acts in the opposite

direction to the displacement, so

the work is negative. Or using the

definition of work (W = F d cos q ),

since q = 180o, then W < 0.

ConcepTest 5.2a Friction and Work I

1) friction does no work at all

2) friction does negative work

3) friction does positive work

A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?

Can friction ever do positive work?

1) yes

2) no

ConcepTest 5.2b Friction and Work II

Can friction ever do positive work?

1) yes

2) no

Consider the case of a box on the back of a pickup truck. If the box moves along with the truck, then it is actually the force of friction that is making the box move.

ConcepTest 5.2b Friction and Work II

In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball?

1) catcher has done positive work2) catcher has done negative work3) catcher has done zero work

ConcepTest 5.2c Play Ball!

In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball?

1) catcher has done positive work2) catcher has done negative work3) catcher has done zero work

The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = F d cos q ), since q = 180o, then W < 0. Note that because the work done on the ball is negative, its speed decreases.

ConcepTest 5.2c Play Ball!

Follow-up: What about the work done by the ball on the catcher?

ConcepTest 5.2d Tension and Work

1) tension does no work at all

2) tension does negative work

3) tension does positive work

A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension?

ConcepTest 5.2d Tension and Work

1) tension does no work at all

2) tension does negative work

3) tension does positive work

A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension?

v

T

No work is done because the force

acts in a perpendicular direction to

the displacement. Or using the

definition of work (W = F d cos q ),

since q = 180o, then W < 0.

Follow-up: Is there a force in the direction of the velocity?

ConcepTest 5.3 Force and Work1) one force

2) two forces

3) three forces

4) four forces

5) no forces are doing work

A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?

ConcepTest 5.3 Force and Work

N

f

T

mg

displacementAny force not perpendicularto the motion will do work:

N does no work

T does positive work

f does negative work

mg does negative work

1) one force

2) two forces

3) three forces

4) four forces

5) no forces are doing work

A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?

ConcepTest 5.8a Slowing Down1) 20 m2) 30 m3) 40 m4) 60 m 5) 80 m

If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases.

F d = Wnet = DKE = 0 – 1/2 mv2

thus: |F| d = 1/2 mv2

Therefore, if the speed doubles,

the stopping distance gets four times larger.

ConcepTest 5.8a Slowing Down1) 20 m2) 30 m3) 40 m4) 60 m 5) 80 m

If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases.

ConcepTest 5.13 Up the Hill1) the same2) twice as much3) four times as much4) half as much5) you gain no PE in either

case

Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path?

Since your vertical position (height) changes by the

same amount in each case, the gain in potential

energy is the same.

ConcepTest 5.13 Up the Hill1) the same2) twice as much3) four times as much4) half as much5) you gain no PE in either

case

Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path?

Follow-up: How much more work do you do in taking the steeper path?

Follow-up: Which path would you rather take? Why?

ConcepTest 5.16 Down the HillThree balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp?

1

4) same speed for all balls2 3

ConcepTest 5.16 Down the Hill

All of the balls have the same initial gravitational PE,

since they are all at the same height (PE = mgh). Thus,

when they get to the bottom, they all have the same final

KE, and hence the same speed (KE = 1/2 mv2).

Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp?

1

4) same speed for all balls

2 3

Follow-up: Which ball takes longer to get down the ramp?

ConcepTest 5.18a Water Slide I1) Paul

2) Kathleen

3) both the same

Paul and Kathleen start from rest at

the same time on frictionless water

slides with different shapes. At the

bottom, whose velocity is greater?

Conservation of Energy: Ei = mgH = Ef = 1/2 mv2

therefore: gH = 1/2 v2

Since they both start from the same height, they have the same velocity at the bottom.

ConcepTest 5.18b Water Slide II

Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. Who makes it to the bottom first?

1) Paul

2) Kathleen

3) both the same

ConcepTest 5.18b Water Slide II

Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. Who makes it to the bottom first?

Even though they both have the same final velocity, Kathleen is at a lower height than Paul for most of her ride. Thus she always has a larger velocity during her ride and therefore arrives earlier!

1) Paul

2) Kathleen

3) both the same

ConcepTest 5.21a Time for Work I

1) Mike

2) Joe

3) both did the same work

Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work?

Both exerted the same force over the same displacement. Therefore, both did the same amount of work. Time does not matter for

determining the work done.

ConcepTest 5.21a Time for Work I

1) Mike

2) Joe

3) both did the same work

Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work?

Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power?

1) Mike produced more power

2) Joe produced more power

3) both produced the same amount of power

ConcepTest 5.21b Time for Work II

Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power?

1) Mike produced more power

2) Joe produced more power

3) both produced the same amount of power

Since power = work / time, we see that Mike produced 0.5 W and Joe produced 0.6 W of power. Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower.

ConcepTest 5.21b Time for Work II

ConcepTest 5.22b Energy Consumption

Which contributes

more to the cost of

your electric bill each

month, a 1500-Watt

hair dryer or a 600-

Watt microwave

oven?

1) hair dryer2) microwave oven3) both contribute equally4) depends upon what you

cook in the oven5) depends upon how long

each one is on

1500 W

600 W

We already saw that what you actually pay for

is energy. To find the energy consumption of

an appliance, you must know more than just

the power rating—you have to know how long

it was running.

ConcepTest 5.22b Energy Consumption

Which contributes more to

the cost of your electric bill

each month, a 1500-Watt hair

dryer or a 600-Watt

microwave oven?

1) hair dryer2) microwave oven3) both contribute equally4) depends upon what you

cook in the oven5) depends upon how long

each one is on

1500 W

600 W

A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s momentum compare to the rate of change of the pebble’s momentum?

1) greater than2) less than3) equal to

ConcepTest 6.3a Momentum and Force

A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s momentum compare to the rate of change of the pebble’s momentum?


The rate of change of momentum is, in fact, the force. Remember that F = Dp/Dt. Since the force exerted on the boulder and the pebble is the same, then the rate of change of momentum is the same.

ConcepTest 6.3a Momentum and Force


ConcepTest 6.3b Velocity and ForceA net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s velocity compare to the rate of change of the pebble’s velocity?


The rate of change of velocity is the acceleration. Remember that a = Dv/Dt. The acceleration is related to the force by Newton’s 2nd Law (F = ma), so the acceleration of the boulder is less than that of the pebble (for the same applied force) because the boulder is much more massive.

ConcepTest 6.3b Velocity and ForceA net force of 200 N acts on a 100 kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s velocity compare to the rate of change of the pebble’s velocity?

ConcepTest 6.4 Collision Course1) the car2) the truck3) they both have the same

momentum change4) can’t tell without knowing the

final velocities

A small car and a large truck collide head-on and stick together. Which one has the larger momentum change?

Since the total momentum of the system is conserved, that means that Dp = 0 for the car and truck combined. Therefore, Dpcar must be equal and

opposite to that of the truck (–Dptruck) in order for the total momentum change to be zero. Note that this conclusion also follows from Newton’s 3rd Law.

ConcepTest 6.4 Collision Course1) the car2) the truck3) they both have the same

momentum change4) can’t tell without knowing the

final velocities

A small car and a large truck collide head-on and stick together. Which one has the larger momentum change?

Follow-up: Which one feels the larger acceleration?

ConcepTest 6.6 Watch Out!You drive around a curve in a narrow one-way street at 30 mph when you see an identical car heading straight toward you at 30 mph. You have two options: hit the car head-on or swerve into a massive concrete wall (also head-on). What should you do?

1) hit the other car2) hit the wall3) makes no difference 4) call your physics

teacher!5) get insurance!

In both cases your momentum will decrease to zero in the collision. Given that the time Dt of the collision is the same, then the force exerted on YOU will be the same!!

If a truck is approaching at 30 mph, then you’d be better off hitting the wall in that case. On the other hand, if it’s only a mosquito, well, you’d be better off running him down...

ConcepTest 6.6 Watch Out!You drive around a curve in a narrow one-way street at 30 mph when you see an identical car heading straight toward you at 30 mph. You have two options: hit the car head-on or swerve into a massive concrete wall (also head-on). What should you do?

1) hit the other car2) hit the wall3) makes no difference 4) call your physics

teacher!5) get insurance!

A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits?

1) the beanbag2) the rubber ball3) both the same

ConcepTest 6.7 Impulse

A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits?

1) the beanbag2) the rubber ball3) both the same

Both objects reach the same speed at the floor. However, while the beanbag comes to rest on the floor, the ball bounces back up with nearly the same speed as it hit. Thus, the change in momentum for the ball is greater, because of the rebound. The impulse delivered by the ball is twice that of the beanbag.

For the beanbag: Dp = pf – pi = 0 – (–mv ) = mv

For the rubber ball: Dp = pf – pi = mv – (–mv ) = 2mv

ConcepTest 6.7 Impulse

Follow-up: Which one imparts the larger force to the floor?

ConcepTest 6.9a Going Bowling I

p

p

1) the bowling ball 2) same time for both3) the ping-pong ball4) impossible to say

A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest?

ConcepTest 6.9a Going Bowling I

We know:

Here, F and Dp are the same for both balls!

It will take the same amount of time to stop them. p

p so Dp = Fav Dt

1) the bowling ball 2) same time for both3) the ping-pong ball4) impossible to say

A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest?

av DtDp

F =

ConcepTest 6.9b Going Bowling II

p

p

A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, for which is the stopping distance greater?

1) the bowling ball 2) same distance for both3) the ping-pong ball4) impossible to say

ConcepTest 6.9b Going Bowling II

p

p

Use the work-energy theorem: W = DKE. The ball with less mass has the greater speed (why?), and thus the greater KE (why again?). In order to remove that KE, work must be done, where W = Fd. Since the force is the same in both cases, the distance needed to stop the less massive ball must be bigger.

A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, for which is the stopping distance greater?

1) the bowling ball 2) same distance for both3) the ping-pong ball4) impossible to say

ConcepTest 6.10a Elastic Collisions I

v 2v

1at rest

at rest

1) situation 1 2) situation 23) both the same

Consider two elastic collisions: 1) a golf ball with speed v hits a stationary bowling ball head-on.

2) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision?

Remember that the magnitude of the relative velocity has to be equal before and after the collision!

ConcepTest 6.10a Elastic Collisions I

v1

In case 1 the bowling ball will almost remain at rest, and the golf ball will bounce back with speed close to v.

v 22v

In case 2 the bowling ball will keep going with speed close to v, hence the golf ball will rebound with speed close to 2v.

1) situation 1 2) situation 23) both the same

Consider two elastic collisions: 1) a golf ball with speed v hits a stationary bowling ball head-on. 2) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision?

ConcepTest 6.10b Elastic Collisions IICarefully place a small rubber ball (mass m) on top of a much bigger basketball (mass M) and drop these from some height h. What is the velocity of the smaller ball after the basketball hits the ground, reverses direction and then collides with small rubber ball?

1) zero 2) v3) 2v4) 3v5) 4v

• Remember that relative velocity has to be equal before and after collision! Before the collision, the basketball bounces up with v and the rubber ball is coming down with v, so their relative velocity is –2v. After the collision, it therefore has to be +2v!!

ConcepTest 6.10b Elastic Collisions II

v

v

v

v

3v

v

(a) (b) (c)

m

M

Carefully place a small rubber ball (mass m) on top of a much bigger basketball (mass M) and drop these from some height h. What is the velocity of the smaller ball after the basketball hits the ground, reverses direction and then collides with small rubber ball?

1) zero 2) v3) 2v4) 3v5) 4v

Follow-up: With initial drop height h, how high does the small rubber ball bounce up?

ConcepTest 6.14b Recoil Speed II1) 0 m/s 2) 0.5 m/s to the right3) 1 m/s to the right4) 20 m/s to the right5) 50 m/s to the right

A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar?

ConcepTest 6.14b Recoil Speed II

Since the initial momentum of the system was zero, the final total momentum must also be zero. Thus, the final momenta of the cannon ball and the flatcar must be equal and opposite.

pcannonball = (10 kg)(50 m/s) = 500 kg-m/s

pflatcar = 500 kg-m/s = (1000 kg)(0.5 m/s)

1) 0 m/s 2) 0.5 m/s to the right3) 1 m/s to the right4) 20 m/s to the right5) 50 m/s to the right

A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar?

When a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. If this is true, then why is the bullet deadly? (whereas it is safe to hold the gun while it is fired)

1) it is much sharper than the gun2) it is smaller and can penetrate your body3) it has more kinetic energy than the gun4) it goes a longer distance and gains speed5) it has more momentum than the gun

ConcepTest 6.15 Gun Control

When a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. If this is true, then why is the bullet deadly? (whereas it is safe to hold the gun while it is fired)

1) it is much sharper than the gun2) it is smaller and can penetrate your body3) it has more kinetic energy than the gun4) it goes a longer distance and gains speed5) it has more momentum than the gun

While it is true that the magnitudes of the momenta of the gun and the bullet are equal, the bullet is less massive and so it has a much higher velocity. Since KE is related to v2, the bullet has considerably more KE and therefore can do more damage on impact.

ConcepTest 6.15 Gun Control

ConcepTest 6.16a Crash Cars I

1) I 2) II3) I and II4) II and III5) all three

If all three collisions

below are totally

inelastic, which one(s)

will bring the car on

the left to a complete

halt?

ConcepTest 6.16a Crash Cars I

In case I, the solid wall clearly stops the car.

In cases II and III, since ptot = 0 before the collision, then ptot must also be zero after the collision, which means that the car comes to a halt in all three cases.

1) I 2) II3) I and II4) II and III5) all three

If all three collisions below

are totally inelastic, which

one(s) will bring the car on

the left to a complete halt?

ConcepTest 6.16b Crash Cars II

If all three collisions below are totally inelastic, which one(s) will cause the most damage (in terms of lost energy)?

1) I 2) II3) III4) II and III5) all three

ConcepTest 6.16b Crash Cars II

The car on the left loses the same KE in all 3 cases, but in case III, the car on the right loses the most KE because KE = 1/2 m v2

and the car in case III has the largest velocity.

If all three collisions below are totally inelastic, which one(s) will cause the most damage (in terms of lost energy)?

1) I 2) II3) III4) II and III5) all three

ConcepTest 6.17 Shut the Door!1) the superball2) the blob of clay3) it doesn’t matter -- they

will be equally effective4) you are just too lazy to

throw anything

You are lying in bed and you want to shut your bedroom door. You have a superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it?

ConcepTest 6.17 Shut the Door!

The superball bounces off the door with almost no loss of speed, so its Dp (and that of the door) is 2mv.

The clay sticks to the door and continues to move along with it, so its Dp is less than that of the superball, and therefore it imparts less Dp to the door.

1) the superball2) the blob of clay3) it doesn’t matter -- they

will be equally effective4) you are just too lazy to

throw anything

You are lying in bed and you want to shut your bedroom door. You have a superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it?

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Physics Semester I