Deck 8: Conservation of Energy

Question 1

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?

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

Answer 1

−2.4 J

Question 2

A baseball is thrown and lands 120 m away. While the ball is in flight, assuming the effect of air friction is negligible, which of the following is true?

A)At maximum height the ball has its greatest kinetic energy.
B)The horizontal component of the baseball's kinetic energy is constant.
C)The vertical component of the baseball's kinetic energy is constant.
D)The mechanical energy of the baseball is greater when nearer to the ground.
E)No answer above is correct.

Answer 2

No answer above is correct.

Question 3

A 10-kg object is dropped from rest. After falling a distance of 50 m, it has a speed of 26 m/s. What is the change in mechanical energy caused by the dissipative (air) resistive force on the object during this descent?

A)−1.3 kJ
B)−1.5 kJ
C)−1.8 kJ
D)−2.0 kJ
E)−2.3 kJ

Answer 3

−1.5 kJ

Question 4

A 1.2-kg mass is projected down a rough circular track (radius = 2.0 m) as shown. The speed of the mass at point A is 3.2 m/s, and at point B, it is 6.0 m/s. What is the change in mechanical energy done on the system between A and B by the force of friction?

A)−8.9 J
B)−7.3 J
C)−8.1 J
D)−6.6 J
E)−24 J

Question 5

The horizontal surface on which the block slides is frictionless. The speed of the block before it touches the spring is 6.0 m/s. How fast is the block moving at the instant the spring has been compressed 15 cm? k = 2.0 kN/m

A)3.7 m/s
B)4.4 m/s
C)4.9 m/s
D)5.4 m/s
E)14 m/s

Question 6

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

Question 7

As a 2.0-kg object moves from m to m, the constant resultant force acting on it is equal to N. If the speed of the object at the initial position is 4.0 m/s, what is its kinetic energy at its final position?

A)62 J
B)53 J
C)73 J
D)86 J
E)24 J

Question 8

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

Question 9

After a skydiver reaches terminal velocity,

A)the force of gravity no longer performs work on the skydiver.
B)work performed by the force of gravity is converted into gravitational potential energy.
C)gravitational potential energy is no longer available to the system of the skydiver plus the Earth.
D)gravitational potential energy is converted into thermal energy.
E)thermal energy is converted into gravitational potential energy.

Question 10

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?

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

Question 11

In a contest, two tractors pull two identical blocks of stone the same distance over identical surfaces. However, block A is moving twice as fast as block B when it crosses the finish line. Which statement is correct?

A)Block A has twice as much kinetic energy as block B.
B)Block B has lost twice as much kinetic energy to friction as block A.
C)Block B has lost twice as much kinetic energy as block A.
D)Both blocks have had equal losses of energy to friction.
E)No energy is lost to friction because the ground has no displacement.

Question 12

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?

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

Question 13

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?

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

Question 14

A moving particle is subject to conservative forces only. When its kinetic energy decreases by 10 J, what happens to its mechanical energy?

A)It increases by 10 J.
B)It decreases by 10 J.
C)It increases, but not necessarily by 10 J.
D)It decreases, but not necessarily by 10 J.
E)It remains the same.

Question 15

If the resultant force acting on a 2.0-kg object is equal to N, what is the change in kinetic energy as the object moves from m to m?

A)+36 J
B)+28 J
C)+32 J
D)+24 J
E)+60 J

Question 16

A 10-kg block on a rough horizontal surface is attached to a light spring (force constant = 1.4 kN/m). The block is pulled 8.0 cm to the right from its equilibrium position and released from rest. The frictional force between the block and surface has a magnitude of 30 N. What is the kinetic energy of the block as it passes through its equilibrium position?

A)4.5 J
B)2.1 J
C)6.9 J
D)6.6 J
E)4.9 J

Question 17

A 2.0-kg block situated on a frictionless incline is connected to a light spring (k = 100 N/m), as shown. The block is released from rest when the spring is unstretched. The pulley is frictionless and has negligible mass. What is the speed of the block when it has moved 0.20 m down the plane?

A)76 cm/s
B)68 cm/s
C)60 cm/s
D)82 cm/s
E)57 cm/s

Question 18

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.

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

Question 19

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)−kx2.
B)− kx2.
C)0.
D)+ kx2.
E)+kx2.

Question 20

A 2.0-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?

A)27 J
B)20 J
C)24 J
D)17 J
E)37 J

Question 21

A 3.50-kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer while the belt moves at a constant speed of 0.200 m/s in the opposite direction. If the coefficient of kinetic friction is 0.400, the magnitude of the mechanical energy dissipated, in J, caused by the force of friction on the block in 8.00 s is

A)5.6.
B)22.0.
C)32.9.
D)54.8.
E)76.8.

Question 22

The work ​ done by the force exerted by the spring on a mass attached to the end of the spring when the mass has displacement is

A)​negative half the time, positive the other half of the time.
B)​always negative.
C)​always positive.
D)​negative more than it is positive.

Question 23

As an object moves from point A to point B only two forces act on it: one force is nonconservative and does −30 J of work, the other force is conservative and does +50 J of work. Between A and B,

A)the kinetic energy of object increases, mechanical energy decreases.
B)the kinetic energy of object decreases, mechanical energy decreases.
C)the kinetic energy of object decreases, mechanical energy increases.
D)the kinetic energy of object increases, mechanical energy increases.
E)None of the above.

Question 24

A mass attached to the end of a spring is pulled out and released on a surface with friction. The work ​ done on the mass by the force exerted by the spring

A)​has the same sign as the change in energy owing to friction during one half of each cycle.
B)​never has the same sign as the change in energy owing to friction.
C)​always has the same sign as the change in energy owing to friction.
D)​never has the same sign as the change in energy owing to friction if the force of friction is greater than the spring force.
E)​always has the same sign as the change in energy owing to friction if the force of friction is greater than the spring force.

Question 25

A 3.50-kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer while the belt moves at a constant speed of 0.200 m/s in the same direction. If the coefficient of kinetic friction is 0.400, the magnitude of the mechanical energy dissipated, in J, caused by the force of friction on the block in 8.00 s is

A)5.6.
B)22.0.
C)32.9.
D)54.8.
E)76.8.

Question 26

The solution to a problem is the equation below. Which description best fits this solution? ​ ​

A)A vertical spring compressed 0.120 m shoots a 2.00-kg mass 2.90 cm above the equilibrium position of the spring.
B)A vertical spring stretched 0.120 m shoots a 2.00-kg mass 9.10 cm above the equilibrium position of the spring.
C)A vertical spring compressed 0.120 m shoots a 2.00-kg mass 12.0 cm above the equilibrium position of the spring.
D)A vertical spring compressed 0.120 m shoots a 2.00-kg mass 14.9 cm above the equilibrium position of the spring.
E)A 2.00-kg mass has fallen 0.820 m and compressed the upper end of a vertical spring 12.0 cm below the equilibrium position.

Question 27

As a result of friction between internal parts of an isolated system

A)the total mechanical energy of the system increases.
B)the total mechanical energy of the system decreases.
C)the total mechanical energy of the system remains the same.
D)the potential energy of the system increases but the kinetic energy remains the same.
E)the kinetic energy of the system increases but the potential energy of the system remains the same.

Question 28

As an object moves from point A to point B only two forces act on it: one force is conservative and does −70 J of work, the other force is nonconservative and does +50 J of work. Between A and B,

A)the kinetic energy of object increases, mechanical energy increases.
B)the kinetic energy of object decreases, mechanical energy increases.
C)the kinetic energy of object decreases, mechanical energy decreases.
D)the kinetic energy of object increases, mechanical energy decreases.
E)None of the above.

Question 29

While running, a person dissipates about 0.6 J of mechanical energy per step per kilogram of body mass. If a 60-kg person runs with a power of 70 watts during a race, how fast is the person running? Assume a running step is 1.5 m long.

Question 30

A 6.0-kg block slides along a horizontal surface. If µk = 0.20 for the block and surface, at what rate is the friction force changing the mechanical energy of the block at an instant when its speed is 4.0 m/s?

A)−59 W
B)−47 W
C)−71 W
D)−82 W
E)+71 W

Question 31

A 1.6-kg block slides down a plane (inclined at 25° with the horizontal) at a constant speed of 2.0 m/s. At what rate is the frictional force changing the mechanical energy of the block?

A)+28 W
B)+13 W
C)−13 W
D)−28 W
E)+6.5 W