KEY NNHS Introductory Physics: MCAS Review Packet #2...KEY NNHS Introductory Physics: MCAS Review Packet #2 Broad Concept: The laws of conservation of energy and momentum provide alternate

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NNHS Introductory Physics: MCAS Review

Packet #2

2. Conservation of Energy and Momentum

Broad Concept: The laws of conservation of energy and momentum provide alternate approaches

to predict and describe the movement of objects.

1.) Which of the following objects has the most

kinetic energy?

A. Toy car with a mass of 1 kg and a speed of

1 m/s.

B. Toy car with a mass of 1 kg and a speed of

5 m/s.

C. Real car with a mass of 1000 kg and a speed

of 1 m/s.

D. Real car with a mass of 1000 kg and a speed

of 5 m/s.

2.) Calculate the kinetic energy of a dog,

mass = 10 kg, running at a speed of 2 m/s.

A. 10 J

B. 20 J

C. 40 J

D. 80 J

My Answer and Explanation:

D. KE= 1/2 * mass * speed

squared.

Bigger mass and bigger speed

means bigger KE.


B. KE=1/2*mass*speed squared

1/2*10*4=20J

Correct Answer and Explanation:


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3.) A person is sitting at rest at the top of the

biggest hill of a rollercoaster. If the person has

a weight of 600 N, and the hill is 30 m high,

what is the person’s gravitational potential

energy?

A. 18000 J

B. 20 J

C. 180000 J

D. 9000 J

4.) You hold a 0.5 kg mass 1 meter above the

ground. Its gravitational potential energy is

approximately:

A. .5 J

B. 5 J

C. 10 J

D. 50 J


A. GPE=Weight*Height

GPE = 600 N * 30 m = 18000 J


B. GPE=mass * 10m/s2 * height

GPE =.5 kg*10m/s2*1 m

GPE = 5 J



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5.) Three different boxes are lifted to different heights. • Box X weighs 115 N and is lifted to 15 m. • Box Y weighs 210 N and is lifted to 10 m. • Box Z weighs 305 N and is lifted to 5 m. Which of the following statements best describes the boxes’ change in mechanical energy? A. Box X had the greatest change in mechanical energy. B. Box Z had the smallest change in mechanical energy. C. Boxes X and Y had the same change in mechanical energy. D. Boxes Y and Z had the same change in mechanical energy.

6.) Which one of the following objects has

mechanical energy (KE +GPE) that remains

constant?

A. A crate being lifted vertically upwards at a

constant velocity.

B. An apple in free-fall.

C. A car accelerating on a level (flat) highway.

D. A sky-diver falling to Earth with his

parachute open.


B.

Box X: Change in GPE

= weight * height

= 115 N * 15 m

= 1725 J

Box Y: Change in GPE

= 210 N * 10 m

= 2100 J

Box Z: Change in GPE

= 305 N * 5 m

= 1525 J


B. An apple in free-fall does

not have air resistance acting

on it. Therefore, as it falls

the GPE is converted to KE and

the total remains constant.



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7.) An astronaut drops a 1.0 kg object and a 5.0

kg object on the Moon. Both objects fall a total

distance of 2.0 m vertically. Which of the

following best describes the objects after they

have fallen a distance of 1.0 m?

A. They have each lost kinetic energy.

B. They have each gained the same amount of

potential energy.

C. They have each lost the same amount of

potential energy.

D. They have each gained one-half of their

maximum kinetic energy.

8.) The figure below shows a wagon that

moves from point X to point Y.

Which of the following best describes the

wagon’s change in energy as it coasts from

point X to point Y?

A. The wagon has the same kinetic energy at

point Y and at point X.

B. The wagon has more kinetic energy at point

Y than at point X.

C. The wagon has the same gravitational

potential energy at point Y and at point X.

D. The wagon has more gravitational potential

energy at point Y than at point X.


D. As the objects fall, their

PE is converted to KE. When

they have fallen 1.0m they are

halfway to the ground. So half

of their GPE has been converted

to KE. So they have gained half

of their KE.


D. At point Y the wagon is

higher above the ground. Thus

it has more GPE than it did at

point X.



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9.) At a weightlifting competition, two

competitors lifted the same weight to the same

height. The second competitor accomplished

the lift 2 seconds faster than the first

competitor. This demonstrated that the second

competitor had more

A. energy than the first.

B. inertia than the first.

C. power than the first.

D. work than the first.

10.) An archer pulls back the bowstring to

prepare to shoot an arrow as shown below.

She uses an average force of 40 N, moving the

bowstring 0.2 m. How much energy is stored

in the bow?

A. 8 J

B. 16 J

C. 24 J

D. 36 J


C. The second competitor has

more power since the same

amount of work was done in less

time:

Power = Work/time.


A. The amount of energy stored

is based on the work done.

W = F*d

= 40 N * 0.2 m = 8 J.



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11.) The Watt is the unit for which quantity:

A. energy

B. work

C. force

D. power

12.) One Joule is equal to

A. One Watt

B. One kg•m/s

C. One Newton-meter

D. One Newton


D. The Watt is the unit for

power.


C. Work is measured in Newton-

meters. Energy is measured in

Joules. Work is a transfer of

energy. Thus you know that

Joules and Newton-meters are

the same.



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13.) What is the mass of an asteroid with a

speed of 200 m/s and a momentum of

2,000 kg•m/s?

A. 10 kg

B. 1,800 kg

C. 2,200 kg

D. 400,000 kg

14.) A bowling ball with a mass of 8.0 kg rolls

down a bowling lane at 2.0 m/s. What is the

momentum of the bowling ball?

A. 4.0 kg • m/s

B. 6.0 kg • m/s

C. 10.0 kg • m/s

D. 16.0 kg • m/s


A. p = m v, so

m = p / v

= (2000 kg m/s) / 200 m/s

= 10 kg


D. p = m v

p = 8 kg * 2 m/s

p = 16 kg m/s



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15.) A student is standing on a skateboard that

is not moving. The total mass of the student

and the skateboard is 50 kilograms. The

student throws a ball with a mass of

2 kilograms forward at 5 m/s. Assuming the

skateboard wheels are frictionless, how will the

student and the skateboard move?

A. forward at 0.4 m/s

B. forward at 5 m/s

C. backward at 0.2 m/s

D. backward at 5 m/s

16.) You are at an ice skating rink and are

gliding towards a friend who is initially at rest.

When you reach your friend, you grab your

friend around the waist and the two of you

continue gliding forward. Which one of the

following is true:

A. Your speed after the collision is greater than

your speed before the collision.

B. Your speed after the collision is the same as

your speed before the collision.

C. Your speed after the collision is smaller

than your speed before the collision.

D. Not enough information has been provided.

My Answer and Explanation: C. Here are two ways to answer:

Conceptual Reasoning: Due to

conservation of momentum, if

the ball is thrown forward, the

student will go backward. Since

the boy has much more mass he

will have much less speed in

order to have the same

momentum.

Mathematical Reasoning: The

total momentum in the system

must remain to be zero so the

momentum of the ball forward

must be equal and opposite to

the momentum of the boy:

pball = 2 kg (5 m/s) = 10 kg m/s

therefore pboy = -10 kg m/s =

(50 kg) v therefore v = (-10 kg

m/s)/(50 kg)

= -0.2m/s, or 0.2m/s backward.


C. When you grab your friend,

your total momentum remains

constant but the amount of mass

that moves is increasing. Thus

your speed must be decreasing.



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17.) An engineering student is gathering data on the motion of a model car traveling down a ramp. If energy is conserved, the potential energy of the car at the top of the ramp should equal the kinetic energy of the car at the bottom of the ramp. After the first trial, the student calculates that the kinetic energy at the bottom of the ramp is less than the potential energy at the top of the ramp. Which of the following can best explain this difference? A. The car gained a small amount of mass as it moved down the ramp. B. The student accidentally accelerated the car at the top of the ramp. C. The measured height of the ramp was less than the actual height. D. The student did not include the effect of frictional force in the calculation.

18.) Mike, who has a mass of 75 kg, is running north at 2.6 m/s. He accidentally collides with Tom, who has a mass of 125 kg and is not moving. Which of the following statements describes how much momentum each person has before the collision? A. Mike has a momentum of 130 kg • m/s north, and Tom has no momentum. B. Mike has a momentum of 195 kg • m/s north, and Tom has no momentum. C. Both Mike and Tom have a momentum of 130 kg • m/s north. D. Both Mike and Tom have a momentum of 195 kg • m/s north.


D. Two ways to answer:

Rule out wrong choices:

Choices A, B, and C would all

result in more KE of the car at

the bottom of the ramp. KE

depends directly on mass and

velocity, and “A” and “B” would

increase those quantities.

Choice “C” would mean the car

lost more GPE, therefore having

more KE at the bottom.

Why D is right:

Friction would do negative

work, which would reduce the

kinetic energy of the car at

the bottom.


B. We can calculate the

momentum each

Person has before the

collision:

Mike: p = m v = 75 kg * 2.6 m/s

= 195 kg m/s

Tom: p = m v = 125 kg * 0 m/s

= zero kg m/s



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Packet #2 Practice: Open-response Question #1

BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION.

Show all your work (diagrams, tables, or computations)

If you do the work in your head, explain in writing how you did the work.

The above diagram shows a simple roller coaster track and one roller coaster car. The car,

when full of passengers, has a mass of 500kg.

A.) If the first hill has a height of 20 meters, calculate the amount of work that must be done to get the full car to the top of the first hill.

B.) If there were no friction, where on this track would the car be going the fastest? Place an x on the spot on the diagram. Explain.

C.) In reality, there is friction on a roller coaster track. Explain why this means that the first hill must be the highest hill on a roller coaster track.

A.) The work done to get the car to the top of the first hill is equal to the amount of energy that the car has at

the top of the hill. The amount of energy at the top of

the first hill is GPE=mgh=500*10*20=100,000Joules

B.) If there were no friction, then the total amount of energy will remain constant. The car will be going the

fastest when it has the most KE. It has the most KE when it

has the least GPE. It has the least GPE at the lowest

height. It has the lowest height at the end. Thus it is

going the fastest at the end.

C.) Since there is friction, energy will continually be lost to heat and sound. Therefore the total amount of energy that

the car has will continually decrease. In order to make it

over a hill, a car needs both GPE and KE. If the total is

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first hill in order to have any KE.

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The illustrations below show an air track with two carts before and after a collision. The mass

and the initial velocity of each cart are shown below.

The first cart slides on the air track and collides with the second cart. The two carts stick together

upon impact and move together along the track, as shown below.

a. What is the momentum of the first cart before it collides with the second cart? Show your

calculations and include units in your answer.

b. What is the momentum of the second cart before the collision? Show your calculations and

include units in your answer.

c. Describe two changes that could be made initially to either one or both carts that would result

in an increase in the momentum of the combined carts after the collision.

A.)

p mv

p 0.2 kg * 0.1m/s

p 0.02 kg m/s

B.)

p mv

p 0.3 kg * 0.050 m/s

p 0.015 kg m/s

C.) You could increase the mass of either one or both of the

carts. You could increase the initial velocity of either one or

both of the carts. Any one of these four changes would increase

Before Collision:

First Cart: mass = 0.20 kg and velocity = 0.10m/s

Second Cart: mass = 0.30 kg and velocity = 0.050m/s

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total amount of momentum after the collision.

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In the diagram below, the falling water turns the waterwheel. The turning waterwheel generates electricity.

The water moves slowly at point A and then falls rapidly past point B. a. Describe the changes in kinetic and gravitational potential energy of the water as it travels from point A to point B. b. Explain why not all of the energy of the moving water available at point A is captured by the waterwheel to generate electricity. c. Describe two ways the system can be changed so that more energy from the falling water is converted into electrical energy.

A.) As the water travels from point A to point B, its gravitational potential energy decreases. While falling

from A to B, its kinetic energy increases.

B.) The waterwheel does not capture all of the energy of the moving water at point A because some of the energy is

used to turn the wheel itself, and that energy is not

available to generate electricity. Also, it appears that

some of the water is splashing and spilling over the water

wheel, so that water would not transfer its energy to the

wheel. Also, some of the energy goes into turbulence and

heating of the water.

C.) To get more energy from the falling water converted into electrical energy, you could build a dam above the

wheel, raising the water level above point A, or move the

wheel lower, so the water would fall from a greater height.

You could build a sluice or channel that would direct all

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Packet #2 the water smoothly onto the wheel, reducing losses due to

spilling and turbulence. If the wheel is made less massive,

with less friction, then less of the water’s energy would

be used to make the wheel turn. Another possibility is to

make the paddles of the wheel more of a “U-shape” rather

than flat, which lengthens the time the water is in

contact, transferring more momentum to the wheel.

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KEY NNHS Introductory Physics: MCAS Review Packet #2...KEY NNHS Introductory Physics: MCAS Review Packet #2 Broad Concept: The laws of conservation of energy and momentum provide alternate