Question 1

The relationship between kilowatt-hours and joules is

Accepted Answer

A)  3.6 x 106 kilowatt-hours = 1 joule. 
B)  3.6 x 106 joules = 1 kilowatt-hour. 
C)  1/3600 kilowatt-hours = 1 joule. 
D)  1/3600 joules = 1 kilowatt-hour. 
A)  3.6 x 106 kilowatt-hours = 1 joule. 
B)  3.6 x 106 joules = 1 kilowatt-hour. 
C)  1/3600 kilowatt-hours = 1 joule. 
D)  1/3600 joules = 1 kilowatt-hour. A

Question 2

Two objects of differing masses $\left( m _ { a } , m _ { b } \right)$ are placed at the top of two frictionless inclines having the same height. Mass $m _ { a }$ is on an incline that makes an angle of $15 ^ { \circ }$ with the horizontal; mass $m _ { b }$ is on an incline that makes an angle of $75 ^ { \circ }$ with the horizontal. The masses are released at the same time. The mass that has the greater acceleration along the incline is:

Accepted Answer

A)  $m _ { a }$ 
B)  $m _ { b }$ 
C)  Both masses have the same acceleration. 
D)  This cannot be determined unless both masses ( $m _ { a } , m _ { b }$ ) are known. 
A)  $m _ { a }$ 
B)  $m _ { b }$ 
C)  Both masses have the same acceleration. 
D)  This cannot be determined unless both masses ( $m _ { a } , m _ { b }$ ) are known. B

Question 3

A 5.6-kg mass is held 5 cm above the end of a vertically oriented linear spring ( $k = 1200$ N/m). The mass is released. The maximum distance that the spring is compressed by the mass is

Accepted Answer

A)  3.6 cm. 
B)  7.5 cm. 
C)  13 cm. 
D)  11 cm. 
A)  3.6 cm. 
B)  7.5 cm. 
C)  13 cm. 
D)  11 cm. C

Question 4

When a mass hanging vertically from a spring attached to the ceiling is in stable equilibrium, the two forms of energy for the system that are at a minimum are

Accepted Answer

A)  the total energy and the gravitational potential energy. 
B)  the kinetic energy and the spring potential energy. 
C)  the spring potential energy and the total energy. 
D)  none of the above. 
A)  the total energy and the gravitational potential energy. 
B)  the kinetic energy and the spring potential energy. 
C)  the spring potential energy and the total energy. 
D)  none of the above.

Question 5

Two objects of differing masses $\left( m _ { a } , m _ { b } \right)$ are placed at the top of two frictionless inclines having the same height. Mass $m _ { a }$ is on an incline that makes an angle of $15 ^ { \circ }$ with the horizontal; mass $m _ { b }$ is on an incline that makes an angle of $75 ^ { \circ }$ with the horizontal. The masses are released at the same time. The mass that reaches the bottom first is

Accepted Answer

A)  $m _ { a }$ 
B)  $m _ { b }$ 
C)  Both masses reach the bottom at the same time. 
D)  This cannot be determined unless both the masses ( $m _ { a } , m _ { b }$ ) are known. 
A)  $m _ { a }$ 
B)  $m _ { b }$ 
C)  Both masses reach the bottom at the same time. 
D)  This cannot be determined unless both the masses ( $m _ { a } , m _ { b }$ ) are known.

Question 6

A 5.6-kg mass is held 5 cm above the end of a vertically oriented linear spring ( $k = 1200$ N/m). The mass is released; it falls, compressing the spring. The spring then expands and does work on the mass. The velocity of the mass as it leaves the spring (in the upward direction) is

Accepted Answer

A)  1 m/s. 
B)  3 m/s. 
C)  4 m/s. 
D)  2 m/s. 
A)  1 m/s. 
B)  3 m/s. 
C)  4 m/s. 
D)  2 m/s.

Question 7

A solid ball $\mathbf { A }$ of mass $m$ and radius $r$ is placed at the top of a smooth, frictionless incline. Another solid ball $\mathbf { B }$ of equal mass and equal radius is placed at the top of a rough incline. Both inclines have the same height $h$ and the same angle. The balls are released at the same time. The ball that reaches the bottom first is

Accepted Answer

A)  ball A. 
B)  ball B. 
C)  Both reach the bottom at the same time. 
D)  This cannot be determined unless $\mu$ of the rough incline is known. 
A)  ball A. 
B)  ball B. 
C)  Both reach the bottom at the same time. 
D)  This cannot be determined unless $\mu$ of the rough incline is known.

Question 8

A solid ball $\mathbf { A }$ of mass $m$ and radius $r$ is placed at the top of a smooth, frictionless incline. Another solid ball $\mathbf { B }$ of equal mass and equal radius is placed at the top of a rough incline. Both inclines have the same height $h$ and the same angle. The balls are released. At the bottom, the ball that has the greater translational kinetic energy is

Accepted Answer

A)  ball A. 
B)  ball B. 
C)  Both have the same. 
D)  This cannot be determined unless $\mu$ of the rough incline is known. 
A)  ball A. 
B)  ball B. 
C)  Both have the same. 
D)  This cannot be determined unless $\mu$ of the rough incline is known.

Question 9

An object of mass $m$ initially at rest is acted upon by a single force $f$ over a distance of $d$. If the single force is the weight of the object, and the distance that the object moved was its original height $( d = h )$, the final kinetic energy of the object is

Accepted Answer

A)  $\mathrm { fh } / \mathrm { m }$ 
B)  $\sqrt { 2 f h / m }$ 
C)  $0$ 
D)  $m g h$ 
A)  $\mathrm { fh } / \mathrm { m }$ 
B)  $\sqrt { 2 f h / m }$ 
C)  $0$ 
D)  $m g h$

Question 10

An object of mass $m$ initially at rest is acted upon by a single force $f$ over a distance of $d$. The final kinetic energy of the object is

Accepted Answer

A)  $f d$ 
B)  $\sqrt { 2 f d / m }$ 
C)  $0$ 
D)  $m g h$ 
A)  $f d$ 
B)  $\sqrt { 2 f d / m }$ 
C)  $0$ 
D)  $m g h$

Question 11

The force to compress a nonlinear spring is given by $F ( x ) = \gamma x ^ { 2 }$, where $\gamma = 45,000 \mathrm {~N} / \mathrm { m } ^ { 2 }$. The amount of energy stored in this spring when it is compressed $10 \mathrm {~cm}$ is

Accepted Answer

A)  450 J. 
B)  220 J. 
C)  45 J. 
D)  15 J. 
A)  450 J. 
B)  220 J. 
C)  45 J. 
D)  15 J.

Question 12

A solid ball having a mass of 2.6 kg and a radius of 0.2 m is placed at the top of an incline. The incline makes an angle of $\theta$ = 51º with the horizontal. The ball is then released and rolls without slipping down the incline. The acceleration of the ball's center of mass along the incline is

Accepted Answer

A)  6.9 m/s $2$ 
B)  6.3 m/s $2$ 
C)  4.5 m/s $2$ 
D)  5.4 m/s $2$ 
A)  6.9 m/s $2$ 
B)  6.3 m/s $2$ 
C)  4.5 m/s $2$ 
D)  5.4 m/s $2$

Question 13

A conservative force

Accepted Answer

A)  may do net work on a body that moves no net distance during the application of the force. 
B)  may change the speed of a body that moves no net distance during the application of the force. 
C)  may do net work on a body undergoing motion confined to a direction perpendicular to the direction of the force. 
D)  may change the direction of motion of a body that moves no net distance during the application of the force. 
A)  may do net work on a body that moves no net distance during the application of the force. 
B)  may change the speed of a body that moves no net distance during the application of the force. 
C)  may do net work on a body undergoing motion confined to a direction perpendicular to the direction of the force. 
D)  may change the direction of motion of a body that moves no net distance during the application of the force.

Question 14

For a conservative force F, all of the following are correct except

Accepted Answer

A)  the line integral of F around a closed path is zero. 
B)  the line integral of F between points A and B by way of point C is independent of point C. 
C)  the line integral of F with limits A and B is independent of the order of the limits. 
D)  there exists an associated potential energy function. 
A)  the line integral of F around a closed path is zero. 
B)  the line integral of F between points A and B by way of point C is independent of point C. 
C)  the line integral of F with limits A and B is independent of the order of the limits. 
D)  there exists an associated potential energy function.

Question 15

Two common forms of energy that cannot be negative are

Accepted Answer

A)  total energy and kinetic energy. 
B)  kinetic energy and gravitational potential energy. 
C)  gravitational potential energy and spring potential energy. 
D)  none of the above. 
A)  total energy and kinetic energy. 
B)  kinetic energy and gravitational potential energy. 
C)  gravitational potential energy and spring potential energy. 
D)  none of the above.

Question 16

When a mass hanging vertically from a spring attached to the ceiling is in stable equilibrium, the two forms of energy for the system that are at a minimum are

Accepted Answer

A)  the total energy and the kinetic energy. 
B)  the kinetic energy and the gravitational potential energy. 
C)  the gravitational potential energy and the spring potential energy. 
D)  none of the above. 
A)  the total energy and the kinetic energy. 
B)  the kinetic energy and the gravitational potential energy. 
C)  the gravitational potential energy and the spring potential energy. 
D)  none of the above.

Question 17

Two common forms of energy that cannot be negative are

Accepted Answer

A)  total energy and gravitational potential energy. 
B)  kinetic energy and spring potential energy. 
C)  spring potential energy and total energy. 
D)  none of the above. 
A)  total energy and gravitational potential energy. 
B)  kinetic energy and spring potential energy. 
C)  spring potential energy and total energy. 
D)  none of the above.

Question 18

The potential energy U is related to the (conservative) force F by an equation of the form

Accepted Answer

A)  U $\propto$  F · dr. 
B)  U $\propto$   Fr dt. 
C)  U $\propto$ dFr/dr. 
D)  U $\propto$ dFr/dt. 
A)  U $\propto$  F · dr. 
B)  U $\propto$   Fr dt. 
C)  U $\propto$ dFr/dr. 
D)  U $\propto$ dFr/dt.

Question 19

A solid ball having a mass of 2.6 kg and a radius of 0.2 m is placed at the top of an incline. The height of the incline is 3.0 m. The ball is then released and rolls without slipping down the incline. The rotational velocity of the ball at the bottom of the incline is

Accepted Answer

A)  32 rad/s. 
B)  26 rad/s. 
C)  19 rad/s. 
D)  12 rad/s. 
A)  32 rad/s. 
B)  26 rad/s. 
C)  19 rad/s. 
D)  12 rad/s.

Question 20

If a force of 1 newton is required to compress a spring 1 meter, the potential energy stored in a spring compressed 2 meters from its uncompressed length is (in joules)

Accepted Answer

A)  0.5. 
B)  1.0. 
C)  2.0. 
D)  4.0. 
A)  0.5. 
B)  1.0. 
C)  2.0. 
D)  4.0.

Exam 8: Conservation of Energy

The relationship between kilowatt-hours and joules is

A 5.6-kg mass is held 5 cm above the end of a vertically oriented linear spring ( k=1200k = 1200k=1200 N/m). The mass is released. The maximum distance that the spring is compressed by the mass is

When a mass hanging vertically from a spring attached to the ceiling is in stable equilibrium, the two forms of energy for the system that are at a minimum are

A 5.6-kg mass is held 5 cm above the end of a vertically oriented linear spring ( k=1200k = 1200k=1200 N/m). The mass is released; it falls, compressing the spring. The spring then expands and does work on the mass. The velocity of the mass as it leaves the spring (in the upward direction) is

An object of mass mmm initially at rest is acted upon by a single force fff over a distance of ddd . If the single force is the weight of the object, and the distance that the object moved was its original height (d=h)( d = h )(d=h) , the final kinetic energy of the object is

An object of mass mmm initially at rest is acted upon by a single force fff over a distance of ddd . The final kinetic energy of the object is

The force to compress a nonlinear spring is given by F(x)=γx2F ( x ) = \gamma x ^ { 2 }F(x)=γx2 , where γ=45,000 N/m2\gamma = 45,000 \mathrm {~N} / \mathrm { m } ^ { 2 }γ=45,000 N/m2 . The amount of energy stored in this spring when it is compressed 10 cm10 \mathrm {~cm}10 cm is

A conservative force

For a conservative force F, all of the following are correct except

Two common forms of energy that cannot be negative are

When a mass hanging vertically from a spring attached to the ceiling is in stable equilibrium, the two forms of energy for the system that are at a minimum are

Two common forms of energy that cannot be negative are

The potential energy U is related to the (conservative) force F by an equation of the form

A solid ball having a mass of 2.6 kg and a radius of 0.2 m is placed at the top of an incline. The height of the incline is 3.0 m. The ball is then released and rolls without slipping down the incline. The rotational velocity of the ball at the bottom of the incline is

If a force of 1 newton is required to compress a spring 1 meter, the potential energy stored in a spring compressed 2 meters from its uncompressed length is (in joules)

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A 5.6-kg mass is held 5 cm above the end of a vertically oriented linear spring ( $k = 1200$ N/m). The mass is released. The maximum distance that the spring is compressed by the mass is

A 5.6-kg mass is held 5 cm above the end of a vertically oriented linear spring ( $k = 1200$ N/m). The mass is released; it falls, compressing the spring. The spring then expands and does work on the mass. The velocity of the mass as it leaves the spring (in the upward direction) is

An object of mass $m$ initially at rest is acted upon by a single force $f$ over a distance of $d$ . If the single force is the weight of the object, and the distance that the object moved was its original height $( d = h )$ , the final kinetic energy of the object is

An object of mass $m$ initially at rest is acted upon by a single force $f$ over a distance of $d$ . The final kinetic energy of the object is

The force to compress a nonlinear spring is given by $F ( x ) = \gamma x ^ { 2 }$ , where $\gamma = 45,000 \mathrm {~N} / \mathrm { m } ^ { 2 }$ . The amount of energy stored in this spring when it is compressed $10 \mathrm {~cm}$ is