Question 1

A block is released from rest at point P and slides along the frictionless track shown. At point Q, its speed is:

Accepted Answer

A)    
B)  2g(h1 - h2) 
C)  (h1 - h2)/2g 
D)    
E)  (h1 - h2)2/2g 
A)    
B)  2g(h1 - h2) 
C)  (h1 - h2)/2g 
D)    
E)  (h1 - h2)2/2g D

Question 2

Given a potential energy function U(x), the corresponding force   is in the positive x direction if:

Accepted Answer

A)  U is positive 
B)  U is negative 
C)  U is an increasing function of x 
D)  U is a decreasing function of x 
E)  it is impossible to obtain the direction of   from U 
A)  U is positive 
B)  U is negative 
C)  U is an increasing function of x 
D)  U is a decreasing function of x 
E)  it is impossible to obtain the direction of   from U D

Question 3

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. When the spring is 4.0 cm longer than its equilibrium length, the speed of the block is 0.50 m/s. The greatest speed of the block is:

Accepted Answer

A)  0.23 m/s 
B)  0.32 m/s 
C)  0.55 m/s 
D)  0.78 m/s 
E)  0.93 m/s 
A)  0.23 m/s 
B)  0.32 m/s 
C)  0.55 m/s 
D)  0.78 m/s 
E)  0.93 m/s D

Question 4

The potential energy of a body of mass m is given by U = -mgx + 1/2kx2. The corresponding force is:

Accepted Answer

A)  -mgx2/2 + kx3/6 
B)  mgx2/2 - kx3/6 
C)  -mg + kx/2 
D)  -mg + kx 
E)  mg - kx 
A)  -mgx2/2 + kx3/6 
B)  mgx2/2 - kx3/6 
C)  -mg + kx/2 
D)  -mg + kx 
E)  mg - kx

Question 5

A toy cork gun contains a spring whose spring constant is 10.0 N/m. The spring is compressed 5.00 cm and then used to propel a 6.00-g cork. The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs. The muzzle velocity of this cork is:

Accepted Answer

A)  1.02 m/s 
B)  1.41 m/s 
C)  2.00 m/s 
D)  2.04 m/s 
E)  4.00 m/s 
A)  1.02 m/s 
B)  1.41 m/s 
C)  2.00 m/s 
D)  2.04 m/s 
E)  4.00 m/s

Question 6

The graphs below show the magnitude of the force on a particle as the particle moves along the positive x axis from the origin to x = x1. The force is parallel to the x axis and is conservative. The maxium magnitude F1 has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive).

Accepted Answer

A)  1, 2, 3 
B)  1, 3, 2 
C)  2, 3, 1 
D)  3, 2, 1 
E)  2, 1, 3 
A)  1, 2, 3 
B)  1, 3, 2 
C)  2, 3, 1 
D)  3, 2, 1 
E)  2, 1, 3

Question 7

The wound spring of a clock possesses:

Accepted Answer

A)  kinetic but no potential energy 
B)  potential but no kinetic energy 
C)  both potential and kinetic energy in equal amonts 
D)  neither potential nor kinetic energy 
E)  both potential and kinetic energy, but more kinetic energy than potential energy 
A)  kinetic but no potential energy 
B)  potential but no kinetic energy 
C)  both potential and kinetic energy in equal amonts 
D)  neither potential nor kinetic energy 
E)  both potential and kinetic energy, but more kinetic energy than potential energy

Question 8

Only if a force on a particle is conservative:

Accepted Answer

A)  is particle is conservative when the particle moves exactly once around any closed path 
B)  is it work equals the change in the kinetic energy of the particle 
C)  it obeys Newton's second law 
D)  it obeys Newton's third law 
E)  it is not a frictional force 
A)  is particle is conservative when the particle moves exactly once around any closed path 
B)  is it work equals the change in the kinetic energy of the particle 
C)  it obeys Newton's second law 
D)  it obeys Newton's third law 
E)  it is not a frictional force

Question 9

A good example of kinetic energy is provided by:

Accepted Answer

A)  a wound-up clock spring 
B)  the raised weights of a grandfather's clock 
C)  a tornado 
D)  a gallon of gasoline 
E)  an automobile storage battery 
A)  a wound-up clock spring 
B)  the raised weights of a grandfather's clock 
C)  a tornado 
D)  a gallon of gasoline 
E)  an automobile storage battery

Question 10

A nonconservative force:

Accepted Answer

A)  violates Newton's second law 
B)  violates Newton's third law 
C)  cannot do any work 
D)  must be perpendicular to the velocity of the particle on which it acts 
E)  none of the above 
A)  violates Newton's second law 
B)  violates Newton's third law 
C)  cannot do any work 
D)  must be perpendicular to the velocity of the particle on which it acts 
E)  none of the above

Question 11

A rectangular block is moving along a frictionless path when it encounters the circular loop as shown. The block passes points 1,2,3,4,1 before returning to the horizontal track. At point 3:

Accepted Answer

A)  its mechanical energy is a minimum 
B)  the forces on it are balanced 
C)  it is not accelerating 
D)  its speed is a minimum 
E)  it experiences a net upward force 
A)  its mechanical energy is a minimum 
B)  the forces on it are balanced 
C)  it is not accelerating 
D)  its speed is a minimum 
E)  it experiences a net upward force

Question 12

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0J/m2)x2 + (2.0J/m4)x4.
When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s. It next stops momentarily to turn around at x =

Accepted Answer

A)  0 
B)  -1.1 m 
C)  1.1 m 
D)  -2.3 m 
E)  2.3 m 
A)  0 
B)  -1.1 m 
C)  1.1 m 
D)  -2.3 m 
E)  2.3 m

Question 13

The thermal energy of a system consisting of a thrown ball, Earth, and the air is most closely associated with:

Accepted Answer

A)  the gravitational interaction of the Earth and the ball 
B)  the kinetic energy of the ball as a whole 
C)  motions of the individual particles within the ball 
D)  motions of individual particles within the ball and the air 
E)  the kinetic energy of Earth as a whole 
A)  the gravitational interaction of the Earth and the ball 
B)  the kinetic energy of the ball as a whole 
C)  motions of the individual particles within the ball 
D)  motions of individual particles within the ball and the air 
E)  the kinetic energy of Earth as a whole

Question 14

A small object slides along the frictionless loop-the-loop with a diameter of 3 m. What minimum speed must it have at the top of the loop?

Accepted Answer

A)  1.9 m/s 
B)  3.8 m/s 
C)  5.4 m/s 
D)  15 m/s 
E)  29 m/s 
A)  1.9 m/s 
B)  3.8 m/s 
C)  5.4 m/s 
D)  15 m/s 
E)  29 m/s

Question 15

The string in the figure is 50 cm long. When the ball is released from rest, it swings along the dotted arc. How fast is it going at the lowest point in its swing?

Accepted Answer

A)  2.0 m/s 
B)  2.2 m/s 
C)  3.1 m/s 
D)  4.4 m/s 
E)  6.0 m/s 
A)  2.0 m/s 
B)  2.2 m/s 
C)  3.1 m/s 
D)  4.4 m/s 
E)  6.0 m/s

Question 16

A 0.20-kg particle moves along the x axis under the influence of a stationary object. The potential energy is given by U(x) = (8.0J/m2)x2 + (2.0J/m4)x4,
Where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is:

Accepted Answer

A)  0 
B)  2.5 m/s 
C)  5.7 m/s 
D)  7.9 m/s 
E)  11 m/s 
A)  0 
B)  2.5 m/s 
C)  5.7 m/s 
D)  7.9 m/s 
E)  11 m/s

Question 17

Two particles interact by conservative forces. This addition, an external force acts on each particle.. They complete round trips, ending at the points where they started. Which of the following must have the same values at the beginning and end of this trip?

Accepted Answer

A)  a total kinetic energy of the two-particle system 
B)  the potential energy of the two-particle system 
C)  the mechanical energy of the two-particle system 
D)  the total linear momentum of the two-particle system 
E)  none of the above 
A)  a total kinetic energy of the two-particle system 
B)  the potential energy of the two-particle system 
C)  the mechanical energy of the two-particle system 
D)  the total linear momentum of the two-particle system 
E)  none of the above

Question 18

Which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x?

Accepted Answer

A)  I 
B)  II 
C)  III 
D)  IV 
E)  V 
A)  I 
B)  II 
C)  III 
D)  IV 
E)  V

Question 19

Two objects interact with each other and with no other objects. Initially object A has a speed of 5 m/s and object B has a speed of 10 m/s. In the course of their motion they return to their initial positions. Then A has a speed of 4 m/s and B has a speed of 7 m/s. We can conclude:

Accepted Answer

A)  the potential energy changed from the beginning to the end of the trip 
B)  mechanical energy was increased by nonconservative forces 
C)  mechanical energy was decreased by nonconservative forces 
D)  mechanical energy was increased by conservative forces 
E)  mechanical energy was decreased by conservative forces 
A)  the potential energy changed from the beginning to the end of the trip 
B)  mechanical energy was increased by nonconservative forces 
C)  mechanical energy was decreased by nonconservative forces 
D)  mechanical energy was increased by conservative forces 
E)  mechanical energy was decreased by conservative forces

Question 20

A 6.0-kg block is released from rest 80 m above the ground. When it has fallen 60 m its kinetic energy is approximately:

Accepted Answer

A)  4800 J 
B)  3500 J 
C)  1200 J 
D)  120 J 
E)  60 J 
A)  4800 J 
B)  3500 J 
C)  1200 J 
D)  120 J 
E)  60 J

Exam 8: Potential Energy and Conservation of Energy

A block is released from rest at point P and slides along the frictionless track shown. At point Q, its speed is:

Given a potential energy function U(x), the corresponding force is in the positive x direction if:

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. When the spring is 4.0 cm longer than its equilibrium length, the speed of the block is 0.50 m/s. The greatest speed of the block is:

The potential energy of a body of mass m is given by U = -mgx + 1/2kx2. The corresponding force is:

A toy cork gun contains a spring whose spring constant is 10.0 N/m. The spring is compressed 5.00 cm and then used to propel a 6.00-g cork. The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs. The muzzle velocity of this cork is:

The wound spring of a clock possesses:

Only if a force on a particle is conservative:

A good example of kinetic energy is provided by:

A nonconservative force:

A rectangular block is moving along a frictionless path when it encounters the circular loop as shown. The block passes points 1,2,3,4,1 before returning to the horizontal track. At point 3:

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0J/m2)x2 + (2.0J/m4)x4. When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s. It next stops momentarily to turn around at x =

The thermal energy of a system consisting of a thrown ball, Earth, and the air is most closely associated with:

A small object slides along the frictionless loop-the-loop with a diameter of 3 m. What minimum speed must it have at the top of the loop?

The string in the figure is 50 cm long. When the ball is released from rest, it swings along the dotted arc. How fast is it going at the lowest point in its swing?

A 0.20-kg particle moves along the x axis under the influence of a stationary object. The potential energy is given by U(x) = (8.0J/m2)x2 + (2.0J/m4)x4, Where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is:

Two particles interact by conservative forces. This addition, an external force acts on each particle.. They complete round trips, ending at the points where they started. Which of the following must have the same values at the beginning and end of this trip?

Which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x?

Two objects interact with each other and with no other objects. Initially object A has a speed of 5 m/s and object B has a speed of 10 m/s. In the course of their motion they return to their initial positions. Then A has a speed of 4 m/s and B has a speed of 7 m/s. We can conclude:

A 6.0-kg block is released from rest 80 m above the ground. When it has fallen 60 m its kinetic energy is approximately:

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The potential energy of a body of mass m is given by U = -mgx + 1/2kx². The corresponding force is:

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0J/m²)x²+ (2.0J/m⁴)x^4. When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s. It next stops momentarily to turn around at x =