Question 1

An all-terrain vehicle of 2000 kg mass moves up a 15.0° slope at a constant velocity of 6.00 m/s. The rate of change of gravitational potential energy with time is

Accepted Answer

A)  5.25 kW. 
B)  24.8 kW. 
C)  30.4 kW. 
D)  118 kW. 
E)  439 kW. 
A)  5.25 kW. 
B)  24.8 kW. 
C)  30.4 kW. 
D)  118 kW. 
E)  439 kW.

Question 2

At what rate is the gravitational force on a 2.0-kg projectile doing work at an instant when the velocity of the projectile is 4.0 m/s directed 30° above the horizontal?

Accepted Answer

A)  +39 W 
B)  −78 W 
C)  −39 W 
D)  +78 W 
E)  +25 W 
A)  +39 W 
B)  −78 W 
C)  −39 W 
D)  +78 W 
E)  +25 W

Question 3

A 12-kg projectile is launched with an initial vertical speed of 20 m/s. It rises to a maximum height of 18 m above the launch point. What is the change in mechanical energy caused by the dissipative (air) resistive force on the projectile during this ascent?

Accepted Answer

A)  −0.64 kJ 
B)  −0.40 kJ 
C)  −0.52 kJ 
D)  −0.28 kJ 
E)  −0.76 kJ 
A)  −0.64 kJ 
B)  −0.40 kJ 
C)  −0.52 kJ 
D)  −0.28 kJ 
E)  −0.76 kJ

Question 4

A 1.2-kg mass is projected up a rough circular track (radius = 0.80 m) as shown. The speed of the mass at point A is 8.4 m/s, and at point B, it is 5.6 m/s. What is the change in mechanical energy between A and B caused by the force of friction?

Accepted Answer

A)  −2.7 J 
B)  −8.8 J 
C)  −4.7 J 
D)  −6.7 J 
E)  −19 J 
A)  −2.7 J 
B)  −8.8 J 
C)  −4.7 J 
D)  −6.7 J 
E)  −19 J

Question 5

As a 1.0-kg object moves from point A to point B, it is acted upon by a single conservative force which does −40 J of work during this motion. At point A the speed of the particle is 6.0 m/s and the potential energy associated with the force is +50 J. What is the potential energy at point B?

Accepted Answer

A)  +72 J 
B)  +10 J 
C)  +90 J 
D)  +28 J 
E)  +68 J 
A)  +72 J 
B)  +10 J 
C)  +90 J 
D)  +28 J 
E)  +68 J

Question 6

A 0.40-kg particle moves under the influence of a single conservative force. At point A where the particle has a speed of 10 m/s, the potential energy associated with the conservative force is +40 J. As the particle moves from A to B, the force does +25 J of work on the particle. What is the value of the potential energy at point B?

Accepted Answer

A)  +65 J 
B)  +15 J 
C)  +35 J 
D)  +45 J 
E)  −40 J 
A)  +65 J 
B)  +15 J 
C)  +35 J 
D)  +45 J 
E)  −40 J

Question 7

A 3.0-kg mass is dropped from the edge of a 50-m tall building with an initial speed of zero. The mass strikes the ground with a downward velocity of 25 m/s. Find the change in mechanical energy of the mass caused by air resistance between the point where it is dropped and the point where it strikes the ground?

Accepted Answer

A)  −0.46 kJ 
B)  −0.53 kJ 
C)  −0.61 kJ 
D)  −0.38 kJ 
E)  −0.81 kJ 
A)  −0.46 kJ 
B)  −0.53 kJ 
C)  −0.61 kJ 
D)  −0.38 kJ 
E)  −0.81 kJ

Question 8

A 2.0-kg block slides down a fixed, rough curved track. The block has a speed of 5.0 m/s after its height above a horizontal surface has decreased by 1.8 m. Assume the block starts from rest. What is the change in mechanical energy of the block caused by the force of friction during this descent?

Accepted Answer

A)  −14 J 
B)  −12 J 
C)  −10 J 
D)  −16 J 
E)  −25 J 
A)  −14 J 
B)  −12 J 
C)  −10 J 
D)  −16 J 
E)  −25 J

Question 9

A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would have used at least ____ J of energy.

Accepted Answer

A)  746 
B)  3.43 × 105 
C)  3.73 × 105 
D)  7.46 × 105 
E)  2.61 × 107 
A)  746 
B)  3.43 × 105 
C)  3.73 × 105 
D)  7.46 × 105 
E)  2.61 × 107

Question 10

Any change of the energy of a system occurs because of

Accepted Answer

A)  energy transfer across the boundaries of the system. 
B)  combustion of fuels within the system. 
C)  radioactive decay of elements within the system. 
D)  all of the above. 
E)  only (b) and (c) above. 
A)  energy transfer across the boundaries of the system. 
B)  combustion of fuels within the system. 
C)  radioactive decay of elements within the system. 
D)  all of the above. 
E)  only (b) and (c) above.

Question 11

A 25-kg block on a horizontal surface is attached to a light spring (force constant = 8.0 kN/m). The block is pulled 10 cm to the right from its equilibrium position and released from rest. When the block has moved 2.0 cm toward its equilibrium position, its kinetic energy is 12 J. What is the change in mechanical energy caused by the frictional force on the block as it moves the 2.0 cm?

Accepted Answer

A)  −4.0 J 
B)  −3.5 J 
C)  −2.4 J 
D)  −2.9 J 
E)  −15 J 
A)  −4.0 J 
B)  −3.5 J 
C)  −2.4 J 
D)  −2.9 J 
E)  −15 J

Question 12

A spring (k = 200 N/m) is suspended with its upper end supported from a ceiling. With the spring hanging in its equilibrium configuration, an object (mass = 2.0 kg) is attached to the lower end and released from rest. What is the speed of the object after it has fallen 4.0 cm?

Accepted Answer

A)  90 cm/s 
B)  79 cm/s 
C)  96 cm/s 
D)  83 cm/s 
E)  57 cm/s 
A)  90 cm/s 
B)  79 cm/s 
C)  96 cm/s 
D)  83 cm/s 
E)  57 cm/s

Question 13

A small lead sphere of mass m is hung from a spring of spring constant k. The gravitational potential energy of the system equals zero at the equilibrium position of the spring before the weight is attached. The total mechanical energy of the system when the mass is hanging at rest is

Accepted Answer

A)  −kx2. 
B)  −
  kx2. 
C)  0. 
D)  +
  kx2. 
E)  +kx2. 
A)  −kx2. 
B)  −
  kx2. 
C)  0. 
D)  +
  kx2. 
E)  +kx2.

Question 14

A surprising demonstration involves dropping an egg from a third-floor window to land on a foam-rubber pad 2 in (5 cm) thick without breaking. If a 56-gram egg falls 12 m, and the foam pad stops the egg in 6.25 ms, by how much is the pad compressed?

Accepted Answer

The answer of A surprising demonstration involves dropping an egg...

Question 15

A simple pendulum, 2.0 m in length, is released from rest when the support string is at an angle of 25° from the vertical. What is the speed of the suspended mass at the bottom of the swing?

Accepted Answer

The answer of A simple pendulum, 2.0 m in length,...

Question 16

A 2.0-kg mass is projected vertically upward from ground level with an initial speed of 30 m/s. The mass rises to a maximum height of 35 m above ground level. What is the change in mechanical energy of the mass caused by air resistance between the point of projection and the point of maximum height?

Accepted Answer

A)  −0.21 kJ 
B)  −0.47 kJ 
C)  −0.40 kJ 
D)  −0.34 kJ 
E)  −0.69 kJ 
A)  −0.21 kJ 
B)  −0.47 kJ 
C)  −0.40 kJ 
D)  −0.34 kJ 
E)  −0.69 kJ

Question 17

A 3.0-kg block is on a frictionless horizontal surface. The block is at rest when, at t = 0, a force (magnitude P = 2.0 N) acting at an angle of 22° above the horizontal is applied to the block. At what rate is the force P doing work at t = 2.0 s?

Accepted Answer

A)  2.3 W 
B)  2.0 W 
C)  1.4 W 
D)  1.7 W 
E)  1.2 W 
A)  2.3 W 
B)  2.0 W 
C)  1.4 W 
D)  1.7 W 
E)  1.2 W

Question 18

Two masses, MA and MB, with MB = 2MA, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen for equal times, we find that

Accepted Answer

A)  KB = KA. 
B)  KB = 2KA. 
C)  KB = 4KA. 
D)  KA = 2KB. 
E)  KA = 4KB. 
A)  KB = KA. 
B)  KB = 2KA. 
C)  KB = 4KA. 
D)  KA = 2KB. 
E)  KA = 4KB.

Question 19

For a force to be a conservative force, when applied to a single test body

Accepted Answer

A)  it must have the same value at all points in space. 
B)  it must have the same direction at all points in space. 
C)  it must be parallel to a displacement in any direction. 
D)  equal work must be done in equal displacements. 
E)  no net work must be done for motion in closed paths. 
A)  it must have the same value at all points in space. 
B)  it must have the same direction at all points in space. 
C)  it must be parallel to a displacement in any direction. 
D)  equal work must be done in equal displacements. 
E)  no net work must be done for motion in closed paths.

Question 20

The two masses in the figure are released from rest. After the 3.0-kg mass has fallen 1.5 m, it is moving with a speed of 3.8 m/s. What is the change in mechanical energy done on the system during this time interval by the frictional force on the 2.0 kg mass?

Accepted Answer

A)  −12 J 
B)  −17 J 
C)  −20 J 
D)  −8.0 J 
E)  −28 J 
A)  −12 J 
B)  −17 J 
C)  −20 J 
D)  −8.0 J 
E)  −28 J

Exam 8: Conservation of Energy

An all-terrain vehicle of 2000 kg mass moves up a 15.0° slope at a constant velocity of 6.00 m/s. The rate of change of gravitational potential energy with time is

At what rate is the gravitational force on a 2.0-kg projectile doing work at an instant when the velocity of the projectile is 4.0 m/s directed 30° above the horizontal?

A 12-kg projectile is launched with an initial vertical speed of 20 m/s. It rises to a maximum height of 18 m above the launch point. What is the change in mechanical energy caused by the dissipative (air) resistive force on the projectile during this ascent?

A 1.2-kg mass is projected up a rough circular track (radius = 0.80 m) as shown. The speed of the mass at point A is 8.4 m/s, and at point B, it is 5.6 m/s. What is the change in mechanical energy between A and B caused by the force of friction?

As a 1.0-kg object moves from point A to point B, it is acted upon by a single conservative force which does −40 J of work during this motion. At point A the speed of the particle is 6.0 m/s and the potential energy associated with the force is +50 J. What is the potential energy at point B?

A 2.0-kg block slides down a fixed, rough curved track. The block has a speed of 5.0 m/s after its height above a horizontal surface has decreased by 1.8 m. Assume the block starts from rest. What is the change in mechanical energy of the block caused by the force of friction during this descent?

A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would have used at least ____ J of energy.

Any change of the energy of a system occurs because of

A spring (k = 200 N/m) is suspended with its upper end supported from a ceiling. With the spring hanging in its equilibrium configuration, an object (mass = 2.0 kg) is attached to the lower end and released from rest. What is the speed of the object after it has fallen 4.0 cm?

A small lead sphere of mass m is hung from a spring of spring constant k. The gravitational potential energy of the system equals zero at the equilibrium position of the spring before the weight is attached. The total mechanical energy of the system when the mass is hanging at rest is

A surprising demonstration involves dropping an egg from a third-floor window to land on a foam-rubber pad 2 in (5 cm) thick without breaking. If a 56-gram egg falls 12 m, and the foam pad stops the egg in 6.25 ms, by how much is the pad compressed?

A simple pendulum, 2.0 m in length, is released from rest when the support string is at an angle of 25° from the vertical. What is the speed of the suspended mass at the bottom of the swing?

A 3.0-kg block is on a frictionless horizontal surface. The block is at rest when, at t = 0, a force (magnitude P = 2.0 N) acting at an angle of 22° above the horizontal is applied to the block. At what rate is the force P doing work at t = 2.0 s?

Two masses, MA and MB, with MB = 2MA, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen for equal times, we find that

For a force to be a conservative force, when applied to a single test body

The two masses in the figure are released from rest. After the 3.0-kg mass has fallen 1.5 m, it is moving with a speed of 3.8 m/s. What is the change in mechanical energy done on the system during this time interval by the frictional force on the 2.0 kg mass?

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Two masses, M_A and M_B, with M_B = 2M_A, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen for equal times, we find that