physics semester i final review. if each component of a vector is doubled, what happens to the angle...

Physics Semester I

Final Review

If each component of a

vector is doubled, what

happens to the angle of

that vector?

1) it doubles

2) it increases, but by less than double

3) it does not change

4) it is reduced by half

5) 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 doubles

2) it increases, but by less than double

3) it does not change

4) it is reduced by half

5) 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 cart

3) it falls in front of the cart

4) it falls right back into the cart

5) it remains at rest

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





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 tilted





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 Package

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

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” ball

2) the “fired” ball

3) they both hit at the same time

4) it depends on how hard the ball was fired

5) 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?



3) they both hit at the same time

4) it depends on how hard the ball was fired

5) 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?



3) neither – they both have the

same velocity on impact

4) it depends on how hard the

ball was thrown

In the previous problem,

which ball has the

greater velocity at

ground level?



3) neither – they both have the

same velocity on impact

4) 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 launched

2) at the highest point in its flight

3) just before it hits the ground

4) 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 launched

2) at the highest point in its flight

3) just before it hits the ground

4) 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 inertia

2) there are no forces acting on it at all

3) it does move, but too slowly to be seen

4) there is no net force on the book

5) 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 inertia

2) there are no forces acting on it at all

3) it does move, but too slowly to be seen

4) there is no net force on the book

5) 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 weight

2) equal to its weight

3) less than its weight but more than zero

4) depends on the speed of the puck

5) 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 weight

2) equal to its weight

3) less than its weight but more than zero

4) depends on the speed of the puck

5) 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 feather

2) it is greater on the stone

3) it is zero on both due to vacuum

4) it is equal on both always

5) 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 feather

2) it is greater on the stone

3) it is zero on both due to vacuum

4) it is equal on both always

5) 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 I

A 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 > mg

2) N = mg

3) 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 I

A 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 > mg

2) N = mg


4) N = 0


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?

1) N > mg

2) N = mg


4) N = 0


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!

1) N > mg

2) N = mg


4) N = 0


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 1

2) case 2

3) it’s the same for both

4) depends on the magnitude of the force F

5) 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 1

2) case 2

3) it’s the same for both

4) depends on the magnitude of the force F

5) depends on the ice surface

ConcepTest 4.11 On an Incline

1) case A

2) case B

3) 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


1) case A

2) case B

3) 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 Incline

Consider two identical blocks,

one resting on a flat surface

and the other resting on an

incline. For which case is the


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 heavy

3) you’re not really pulling down – it just seems that way

4) the rope actually pulls you up

5) 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 heavy

3) you’re not really pulling down – it just seems that way

4) the rope actually pulls you up

5) 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 car

2) the truck

3) both the same

4) it depends on the velocity of each

5) 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?

1) the car

2) the truck

3) both the same



According to Newton’s Third Law, both vehicles

experience the same magnitude of force.

1) the car

2) the truck

3) both the same



In the collision

between the

car and the

truck, which

has the greater

acceleration?

ConcepTest 4.14b Collision Course II

1) the car

2) the truck

3) both the same



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 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 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 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 4.22 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 ms =

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 (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 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 ms = 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 (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 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 4.23a Sliding 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 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 = 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 work

2) catcher has done negative work

3) 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 work

2) catcher has done negative work

3) 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 = 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 = 180o, then W < 0.

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

ConcepTest 5.3 Force and 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 5.3 Force and Work

N

f

T

mg

displacementAny force not perpendicular

to 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 Down

1) 20 m

2) 30 m

3) 40 m

4) 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 Down

1) 20 m

2) 30 m

3) 40 m

4) 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 Hill

1) the same

2) twice as much

3) four times as much

4) half as much

5) 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 Hill

1) the same

2) twice as much

3) four times as much

4) half as much

5) 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 Hill

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 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 balls2 3

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

ConcepTest 5.18a Water Slide I

1) 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 dryer

2) microwave oven

3) both contribute equally

4) depends upon what you cook in the oven

5) 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 dryer

2) microwave oven

3) both contribute equally

4) depends upon what you cook in the oven

5) 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 than

2) less than

3) equal to

ConcepTest 6.3a Momentum and Force





boulder’s momentum compare to

the rate of change of the pebble’s

momentum?

1) greater than

2) less than

3) equal to

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

1) greater than

2) less than

3) equal to

ConcepTest 6.3b Velocity and Force





boulder’s velocity compare to the

rate of change of the pebble’s

velocity?

1) greater than

2) less than

3) equal to

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 Force

A net force of 200 N acts on a 100 kg




boulder’s velocity compare to the

rate of change of the pebble’s

velocity?

ConcepTest 6.4 Collision Course

1) the car

2) the truck

3) they both have the same

momentum change

4) 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 Course

1) the car

2) the truck

3) they both have the same

momentum change

4) 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 car

2) hit the wall

3) 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 car

2) hit the wall

3) 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 beanbag

2) the rubber ball

3) 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 beanbag

2) the rubber ball

3) 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 both

3) the ping-pong ball

4) 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 both



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 both



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 both



ConcepTest 6.10a Elastic Collisions I

v 2

v

1at rest

at rest

1) situation 1

2) situation 2

3) 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

v

1

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

v 2

2v

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 2

3) 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 II

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) v

3) 2v

4) 3v

5) 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) v

3) 2v

4) 3v

5) 4v

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

ConcepTest 6.14b Recoil Speed II

1) 0 m/s

2) 0.5 m/s to the right

3) 1 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 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 gun

2) it is smaller and can penetrate your body

3) it has more kinetic energy than the gun

4) it goes a longer distance and gains speed

5) 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 gun

2) it is smaller and can penetrate your body

3) it has more kinetic energy than the gun

4) it goes a longer distance and gains speed

5) 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) II

3) I and II

4) II and III

5) 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) II

3) I and II

4) II and III

5) 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) II

3) III

4) II and III

5) 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) II

3) III

4) II and III

5) all three

ConcepTest 6.17 Shut the Door!

1) the superball

2) the blob of clay

3) it doesn’t matter -- they

will be equally effective

4) 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 superball

2) the blob of clay

3) it doesn’t matter -- they

will be equally effective

4) 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?

physics semester i final review. if each component of a vector is doubled, what happens to the angle...

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