Download Chapter 4 X1

Chapter 4 X1 - X5
Multiple Choice
Identify the choice that best completes the statement or answers the question. You can use 10 m/s2 for g for these
questions.
1. Three people of equal mass climb a mountain using paths A, B, and C shown in the diagram below. Along which
path(s) does a person gain the greatest amount of gravitational potential energy from start to finish?
a.
b.
c.
d.
path A, only
path B, only
path C, only
The gain is the same along all paths.
2. If the velocity of an automobile is doubled, its kinetic energy:
a. decreases to one-half.
b. doubles.
c. decreases to one-fourth.
d. quadruples.
3. A car of mass M on a frictionless track starts from rest at the top of a hill having height h1, as shown in the
diagram below. What is the kinetic energy of the train when it reaches the top of the next hill, having height h2?
a.
b.
c.
d.
Mg(h2h3)
Mgh1
0
Mg(h1-h2)
The diagram below represents a 2.0-kg mass placed on a frictionless track at point A and released from rest.
Assume the gravitational potential energy of the system to be zero at point E.
4. What is the approximate gravitational potential energy of the system at point A?
a. 20. J
b. 7.0  10 J
c. 80. J
d. 8.0  10 J
2
2
5. Compared to the kinetic energy of the mass at point B, the kinetic energy of the mass at point F is:
a. the same.
b. one-half as great.
c. four times as great.
d. twice as great.
6. If the mass were released from rest at point B, its speed at point C would be:
a. 14 m/s
b. 10. m/s
c. 0 m/s.
d. 0.50 m/s
7. As the mass travels along the track, the maximum height it will reach above point E will be closest to:
a. 20. m.
b. 30. m.
c. 10. m.
d. 40. m.
8. A spring has a spring constant of 120. N/m. How much potential energy is stored in the spring as it is stretched
0.20 meter?
a. 4.8 J
b. 2.4 J
c. 12 J
d. 24 J
9. Energy is measured in the same units as:
a. work.
b. momentum.
c. power.
d. force.
The diagram below represents a 1.00-kg object being held at rest on a frictionless incline.
10. The object is released and slides the length of the incline. When it reaches the bottom of the incline, the object’s
kinetic energy will be closest to:
a. 2.00 J
b. 4.00 J
c. 9.81 J
d. 19.6 J.
11. As the object slides down the incline, the sum of the gravitational potential energy and kinetic energy of the object:
a. will increase.
b. will decrease.
c. cannot be determined from the information provided.
d. will remain the same.
12. Which graph best represents the relationship between the elongation of an ideal spring and the applied force?
a.
c.
b.
d.
13. The spring of a toy car is wound by pushing the car backward with an average force of 15 newtons through a
distance of 0.50 meter. How much elastic potential energy is stored in the car’s spring during this process?
a. 30. J
b. 56 J
c. 1.9 J
d. 7.5 J
14. The graph below represents the relationship between the force applied to a spring and the elongation of the spring.
What is the value of the spring constant?
a.
b.
c.
d.
0.80 m
0.050 m/N
20. N/m
9.8 N/kg
15. The diagram below represents a block suspended from a spring. The spring is stretched 0.200 m. If the spring
constant is 200. N/m, what is the weight of the block?
a.
b.
c.
d.
20.0 N
8.00 N
4.00 N
40.0 N
16. As an object falls freely near the Earth’s surface, the loss in gravitational potential energy of the object is equal to
its:
a. gain in kinetic energy.
b. loss of height.
c. loss of mass.
d. gain in velocity.
In the diagram below, an ideal pendulum released from point A swings freely through point B.
17.
Compared to the pendulum's kinetic energy at A, its potential energy at B is:
a. twice as great.
b. four times as great.
c. half as great.
d. the same.
18. As the pendulum swings from position A to position B as shown in the diagram below, what is the relationship of
kinetic energy to potential energy? [Neglect friction.]
a. The kinetic energy increase is more than the potential energy decrease.
b. The kinetic energy decrease is equal to the potential energy increase.
c. The kinetic energy increase is equal to the potential energy decrease.
d. The kinetic energy decrease is more than the potential energy increase.
19. If the pendulum has a total energy of 4 J, which statement below correctly describes the kinetic and graviational
potential energies of the pendulum system as the ball swings back and forth?
a. The kinetic energy at the botom is 4 J and the potential energy at the top is zero.
b. The kinetic energy at the botom is zero and the potential energy at the top is 4J.
c. The kinetic energy at the botom is 4 J and the potential energy at the top is 4J.
d. The kinetic energy at the botom is 2 J and the potential energy at the top is 2J
20. The diagram below shows a 0.1-kilogram apple attached to a branch of a tree 2 meters above a spring placed on the
ground below. The apple falls and hits the spring, compressing the spring 0.1 meters from its rest position. If all of
the gravitational potential energy of the apple on the tree is transferred to the spring when it is compressed, what is
the spring constant of the spring?
a.
b.
c.
d.
10 N/m
400 N/m
100 N/m
40 N/m
21. The graph below represents the kinetic energy, gravitational potential energy, and the total mechanical energy of a
moving block. Which best describes the motion of the block?
a. falling freely
b. accelerating on a flat horizontal surface
c. being lifted at a constant velocity
d. sliding up a frictionless incline
22. A car initially traveling at a speed of 16 m/s accelerates uniformly to a speed of 20. m/s over a distance of 36
meters. What is the magnitude of the car’s acceleration?
a. 0.11 m/s
b. 0.22 m/s
c. 9.0 m/s
d. 2.0 m/s
2
2
2
2
23. In the diagram below, a 20.0-newton force is used to push a 2.00-kilogram cart a distance of 5.00 meters. How
much work was done on the cart?
a.
b.
c.
d.
40.0 J
200. J
150. J
100. J
24. A 1.0-kilogram rubber ball traveling east at 4.0 meters per second hits a wall and bounces back toward the west at
2.0 meters per second. Compared to the kinetic energy of the ball before it hits the wall, the kinetic energy of the
ball after it bounces off the wall is:
a. one-fourth as great.
b. one-half as great.
c. four times as great.
d. the same.
25. The graph below represents the relationship between gravitational force and mass for objects near the surface of
Earth. The slope of the graph represents the:
a.
b.
c.
d.
momentum of the object.
universal gravitational constant.
weight of the object.
acceleration due to gravity.
26. The graph below shows elongation as a function of the applied force for two springs, A and B. Which statement is
correct?
a.
b.
c.
d.
The same force is required to stretch spring B and spring A the same distance.
A greater force is required to stretch spring A than spring B the same distance.
The spring constant for spring B is larger than for spring A.
Spring A is stiffer than spring B.
27. What is an essential characteristic of an object in equilibrium?
a. zero potential energy
b. zero acceleration
c. zero velocity
d. zero kinetic energy
28. Which graph best represents the elastic potential energy stored in a spring, PE, as a function of its elongation, x?
a.
c.
b.
d.
29. A spring is stretched. Which statement is correct?
a. The spring constant of the spring increases.
b. The spring’s elastic potential energy is increased.
c. The force required to complete the stretching decreases.
d. The displacement of the spring remains the same.
30. What is the approximate mass of an apple that weighs 1 newton on the surface of Earth?
a.
b.
c.
d.
100 kg
0.1 kg
10 kg
1 kg
31. As the distance an object is above Earth increases, what happens to the gravitational force between the object and
Earth?
a. The force increases linearly.
b. The force decreases exponentially.
c. The force increases exponentially.
d. The force remains the same.
32. According to Newton’s Law of Universal Gravitation, the gravitational force between two masses is proportional
to the product of the two masses and:
a. becomes stronger as the density of the masses decreases.
b. becomes stronger as the masses are moved a greater distance apart.
c. becomes stronger as the masses becomes larger.
d. becomes stronger as time progresses.
33. The gravitational force between two asteroids is 500. newtons. What would the force be if the distance between the
two asteroids doubled?
a. 250. N
b. 125 N
c. 2,000 N
d. 500. N
34. A satellite sitting on a launch pad is one Earth radius away from the center of the Earth. How would the
gravitational force between the satellite and Earth change after launch when the satellite is two Earth radii from the
center of Earth?
a. The force would be 2 times greater.
b. The force would be 1/4 as great.
c. The force would be 4 times greater.
d. The force would be 1/2 as great.
35. A 0.20 kg mass hangs on the end of a spring. The spring stretches 0.30 m. What is the weight of the mass on the
spring?
a. 1.5 N
b. 2.0 N
c. 3.0 N
d. 6.0 N
36. A different mass now hangs on the above spring and the spring stretches to a length of 0.75 m. According to
Hooke’s law, what is the value of this new mass?
a. 0.75 kg
b. 0.60 kg
c. 0.5 kg
d. 0.4 kg
37. A roller coaster undergoes different changes in vleocity during the ride, with each change taking one second.
WHich change in velocity would cause a passenger to experience the greatest magnitude of acceleration?
a. 20 m/s to 24 m/s
b. 16 m/s to 22 m/s
c. 4 m/s to 8 m/s
d. 2 m/s to 6 m/s
38. A ride on a roller coaster with a 900-m track lasts two minutes. What are a passenger’s average speed and average
velocity for the ride?
a. Both speed and velocity are 7.5 m/s.
b. The average speed is 7.5 m/s and average velocity are zero.
c. The average speed is zero and average velocity are 7.5 m/s.
d. The average speed is zero and average velocity are zero.
39. A ball starts from rest and rolls down an inclined track toward a photogate. If the mass is already known, the data
from the photogate makes it possible to calculate the
a. kinetic energy and starting gravitational potential energy
b. potential energy and the ball’s acceleration
c. kinetic energy and the ball’s acceleration
d. ball’s acceleration and starting gravitational potential energy
40. A pop-up toy with a spring constant of 100 N/m and a mass of 0.005 kg is compressed 0.02 m. What is the toy’s
spring potential energy?
a. 1 J
b. 5J
c. 0.02 J
d. 0.0005J
Problem: Solve each of the following problems, showing ALL work in order to receive full credit. Minimum work
required includes the equation used, the values plugged in, and the answer with correct units.
1. A cart with a mass of 0.5 kg is at the top of a 0.4 m high ramp.
a) What would be the cart’s velocity at the bottom of the ramp?
b) How much work would be required to bring the cart back up to the top of the ramp?
2. A pop-up toy with a spring constant of 50 N/m and a mass of 0.005 kg is compressed 0.04 m, and then released.
a) If all the
spring potential energy is converted to gravitational potential energy, how high will the toy pop up?
b)How fast is the
toy moving when the spring has popped fully?
3. The data below pertains to the stretch of a spring given the amount of mass hanging from it.
a) Graph the data above.
b) Using the data, calculate the spring constant of the spring.
c) Calculate the spring potential energy of the spring when it is stretched a distance of 0.80 m.
d) If a 0.500-kg mass were suspended from the spring, how far would the spring stretch?
4. The Moon is 60 times further away from the center of the Earth than objects on the surface of the Earth, and moves
about the Earth in an approximately circular path.
a) Use the inverse square law to determine the acceleration due to gravity at the Moon’s position.
b) Find the speed of the Moon if the Moon is 3.84 x 108 m away from the center of the Earth and its period is 28.25
days.
c) Calculate the acceleration of the Moon using the speed from Part (b).
Chapter 4 X1 - X5
Answer Section
MULTIPLE CHOICE
1. ANS:
NAT:
TOP:
KEY:
2. ANS:
NAT:
TOP:
KEY:
3. ANS:
NAT:
TOP:
KEY:
4. ANS:
NAT:
TOP:
KEY:
5. ANS:
NAT:
TOP:
KEY:
6. ANS:
NAT:
TOP:
KEY:
7. ANS:
NAT:
TOP:
KEY:
8. ANS:
NAT:
KEY:
9. ANS:
NAT:
KEY:
10. ANS:
NAT:
TOP:
KEY:
11. ANS:
NAT:
TOP:
KEY:
12. ANS:
D
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
potential energy
D
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
kinetic energy
D
PTS: 1
DIF: Difficult
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
kinetic energy
D
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
kinetic energy
D
PTS: 1
DIF: Difficult
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
potential energy
C
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
kinetic energy
D
PTS: 1
DIF: Difficult
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
potential energy
B
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
TOP: Section 3 Spring Potential Energy
spring
A
PTS: 1
DIF: Easy
Conservation of energy and increase in disorder
TOP: Section 3 Spring Potential Energy
work
D
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
kinetic energy
D
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
kinetic energy
C
PTS: 1
DIF: Medium
NAT: Motion and Forces
TOP:
13. ANS:
TOP:
14. ANS:
TOP:
15. ANS:
TOP:
16. ANS:
NAT:
TOP:
17. ANS:
NAT:
TOP:
KEY:
18. ANS:
NAT:
TOP:
KEY:
19. ANS:
20. ANS:
NAT:
KEY:
21. ANS:
NAT:
TOP:
KEY:
22. ANS:
TOP:
23. ANS:
NAT:
KEY:
24. ANS:
NAT:
TOP:
KEY:
25. ANS:
TOP:
26. ANS:
TOP:
27. ANS:
TOP:
28. ANS:
NAT:
TOP:
29. ANS:
NAT:
KEY:
30. ANS:
TOP:
Section 3 Spring Potential Energy
KEY:
D
PTS: 1
DIF: Medium
NAT:
Section 3 Spring Potential Energy
KEY:
C
PTS: 1
DIF: Medium
NAT:
Section 5 Hooke's Law: Your At Rest Weight
KEY:
D
PTS: 1
DIF: Medium
NAT:
Section 5 Hooke's Law: Your At Rest Weight
KEY:
A
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
Section 5 Hooke's Law: Your At Rest Weight
KEY:
D
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
pendulum
C
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
pendulum
C
PTS: 1
B
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
TOP:
potential energy
A
PTS: 1
DIF: Difficult
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
kinetic energy
D
PTS: 1
DIF: Medium
NAT:
Section 1 Velocity and Acceleration: The Big Thrill
KEY:
D
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
TOP:
work
A
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
Section 2 Gravitational Potential Energy and Kinetic Energy
kinetic energy
D
PTS: 1
DIF: Medium
NAT:
Section 5 Hooke's Law: Your At Rest Weight
KEY:
C
PTS: 1
DIF: Medium
NAT:
Section 5 Hooke's Law: Your At Rest Weight
KEY:
B
PTS: 1
DIF: Medium
NAT:
Section 1 Velocity and Acceleration: The Big Thrill
KEY:
B
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
Section 5 Hooke's Law: Your At Rest Weight
KEY:
B
PTS: 1
DIF: Medium
Conservation of energy and increase in disorder
TOP:
potential energy
B
PTS: 1
DIF: Medium
NAT:
Section 10 Safety is Required but Thrills are Desired
KEY:
spring
Motion and Forces
potential energy
Motion and Forces
force
Motion and Forces
spring
potential energy
Section 3 Spring Potential Energy
Motion and Forces
acceleration
Section 8 Work and Power
Motion and Forces
acceleration
Motion and Forces
force
Motion and Forces
equilibrium
potential energy
Section 3 Spring Potential Energy
Motion and Forces
weight
31. ANS:
TOP:
32. ANS:
TOP:
33. ANS:
TOP:
34. ANS:
TOP:
35. ANS:
36. ANS:
37. ANS:
38. ANS:
39. ANS:
40. ANS:
B
PTS: 1
DIF: Medium
Section 4 Newton's Law of Universal Gravitation
C
PTS: 1
DIF: Medium
Section 4 Newton's Law of Universal Gravitation
B
PTS: 1
DIF: Medium
Section 4 Newton's Law of Universal Gravitation
B
PTS: 1
DIF: Medium
Section 4 Newton's Law of Universal Gravitation
B
PTS: 1
C
PTS: 1
B
PTS: 1
A
PTS: 1
C
PTS: 1
C
PTS: 1
PROBLEM
1. ANS:
a) mgh = 1/2 mv2
9.8 * 0.4 = 1/2 v2
2.8 m/s = v
b) W = GPE = 0.5 * 9.8 * 0.4 = 1.96 J
PTS: 1
2. ANS:
EPE=GPE
1/2 *50*0.04^2 = 0.005 * 9.8 *h
0.04 = 0.049 * h
0.816 m = h
EPE=KE
1/2 *50*0.04^2 = 1/2 (0.005) * v^2
0.04 = 0.0025*v^2
16 m/s = v
PTS: 1
3. ANS:
d
PTS: 1
4. ANS:
x
PTS: 1
NAT:
KEY:
NAT:
KEY:
NAT:
KEY:
NAT:
KEY:
Motion and Forces
gravity
Motion and Forces
gravity
Motion and Forces
gravity
Motion and Forces
gravity