Deck 6: Conservation of Energy

Question 1

A $20.0 \mathrm{~N}$ force is applied at an angle of 40.0 degrees above the horizontal to a $4.00 \mathrm{~kg}$ box. The box moves a horizontal distance of 4.00 meters. Friction is negligible. The work done by the $20.0 \mathrm{~N}$ force is

A) $46.3 \mathrm{~J}$ .
B) $50.1 \mathrm{~J}$ .
C) $75.0 \mathrm{~J}$ .
D) $40.5 \mathrm{~J}$ .
E) $61.3 \mathrm{~J}$ .

Answer 1

$61.3 \mathrm{~J}$ .

Question 2

A $6.00 \mathrm{~kg}$ box is pulled up an $8.00 \mathrm{~m}$ long incline (with friction) at an angle of 30.0 degrees by a force of $50.0 \mathrm{~N}$ parallel to the incline. The coefficient of kinetic friction is 0.100 . The work done against friction is

A) $40.7 \mathrm{~J}$ .
B) $30.3 \mathrm{~J}$ .
C) $22.0 \mathrm{~J}$ .
D) $26.5 \mathrm{~J}$ .
E) $35.2 \mathrm{~J}$

Answer 2

$40.7 \mathrm{~J}$ .

Question 3

The graph shows the force on an object as it moves a distance $x$ . What is the work done by the force as the object moves from $2.0 \mathrm{~m}$ to $8.0 \mathrm{~m}$ ?

A) $52 \mathrm{~J}$
B) $50 \mathrm{~J}$
C) $35 \mathrm{~J}$
D) $60 \mathrm{~J}$
E) $48 \mathrm{~J}$

Answer 3

$48 \mathrm{~J}$

Question 4

The graph shows the force on an object as it moves a distance $\mathrm{x}$ . What is the work done by the force as the object moves from $0.0 \mathrm{~m}$ to $6.0 \mathrm{~m}$ ?

A) $8.0 \mathrm{~J}$
B) $14 \mathrm{~J}$
C) $12 \mathrm{~J}$
D) $6.0 \mathrm{~J}$
E) $10 \mathrm{~J}$

Question 5

A 5.00 gram bullet has a velocity of $300 \mathrm{~m} / \mathrm{s}$ . It strikes a block of wood and penetrates to a depth of 2.00 $\mathrm{cm}$ . The average force of the block of wood on the bullet is

A) $21,400 \mathrm{~N}$ .
B) $11,250 \mathrm{~N}$ .
C) $15,200 \mathrm{~N}$ .
D) $9,340 \mathrm{~N}$ .
E) $19,500 \mathrm{~N}$ .

Question 6

A $2,000 \mathrm{~kg}$ car traveling at $30.0 \mathrm{mi} / \mathrm{h}$ skids to a stop in 60.0 meters. The force of friction during the skid is $(1.0 \mathrm{mi} / \mathrm{h}=0.447 \mathrm{~m} / \mathrm{s})$

A) $2,400 \mathrm{~N}$ .
B) $3,000 \mathrm{~N}$ .
C) $4,200 \mathrm{~N}$ .
D) $3,750 \mathrm{~N}$
E) $4,500 \mathrm{~N}$

Question 7

The explosion in a cannon exerts an average force of $30,000 \mathrm{~N}$ for $\mathrm{L}$ meters, the length of the cannon. What length of the cannon would be necessary to shoot a $2.0 \mathrm{~kg}$ projectile from the surface of the Earth to a distance of $6.84 \times 10^{8} \mathrm{~m}$ from the center of the Earth (the same as the distance to the Moon)? $(\mathrm{G}=6.67 \times$ $10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg} 2, \mathrm{ME}=5.97 \times 10^{24} \mathrm{~kg}$ , and $\mathrm{RE}=6.37 \times 10^{6} \mathrm{~m}$ .)

A) $3.9 \mathrm{~km}$ .
B) $4.1 \mathrm{~km}$ .
C) $5.0 \mathrm{~km}$ .
D) $3.0 \mathrm{~km}$ .
E) $2.7 \mathrm{~km}$ .

Question 8

A $20.0 \mathrm{~kg}$ box slides down a $12.0 \mathrm{~m}$ long incline at an angle of 30.0 degrees with the horizontal. A force of $50.0 \mathrm{~N}$ is applied to the box to try to prevent it from sliding down the incline. The applied force makes an angle of 10.00 degrees to the incline and above the incline. If the incline has a coefficient of kinetic friction of 0.100 , then the increase in the kinetic energy of the box is

A) $392 \mathrm{~J}$ .
B) $300 \mathrm{~J}$ .
C) $275 \mathrm{~J}$ .
D) $203 \mathrm{~J}$ .
E) $425 \mathrm{~J}$ .

Question 9

A $20.0 \mathrm{~kg}$ box slides down a $12.0 \mathrm{~m}$ long incline at an angle of 3.0 degrees with the horizontal. A force of $50.0 \mathrm{~N}$ is applied to the box to try to prevent it from sliding down the incline. The applied force makes an angle of 0.00 degrees to the incline. If the incline has a coefficient of kinetic friction of 0.100 , then the increase in the kinetic energy of the box is

A) $525 \mathrm{~J}$ .
B) $455 \mathrm{~J}$ .
C) $300 \mathrm{~J}$ .
D) $372 \mathrm{~J}$ .
E) $410 \mathrm{~J}$ .

Question 10

A $20.0 \mathrm{~kg}$ box slides down a $12.0 \mathrm{~m}$ long incline at an angle of 30.0 degrees with the horizontal. A force of $50.0 \mathrm{~N}$ is applied to the box in the upward direction to try to prevent it from sliding down the incline. The applied force makes an angle of 10.0 degrees to the incline. If the incline has no friction, then the increase in the kinetic energy of the box is

A) $420 \mathrm{~J}$ .
B) $475 \mathrm{~J}$ .
C) $585 \mathrm{~J}$ .
D) $521 \mathrm{~J}$ .
E) $620 \mathrm{~J}$ .

Question 11

A $2500 \mathrm{~kg}$ car accelerates from rest to a velocity of $30.0 \mathrm{~m} / \mathrm{s}$ in 8.00 seconds. The work done by the engine to accelerate the car is

A) $1.13 \times 106 \mathrm{~J}$ .
B) $2.01 \times 106 \mathrm{~J}$ .
C) $1.85 \times 106 \mathrm{~J}$ .
D) $3.10 \times 106 \mathrm{~J}$ .
E) $2.56 \times 106 \mathrm{~J}$ .

Question 12

A $3.00 \mathrm{~kg}$ pendulum bob on a string $2.00 \mathrm{~m}$ long is released with a velocity of $2.00 \mathrm{~m} / \mathrm{s}$ when the support string makes an angle of 45.0 degrees with the vertical. What is the tension in the string at the highest point of its motion?

A) $31.6 \mathrm{~N}$
B) $12.5 \mathrm{~N}$
C) $28.9 \mathrm{~N}$
D) $17.8 \mathrm{~N}$
E) $21.4 \mathrm{~N}$

Question 13

A $2.00 \mathrm{~kg}$ pendulum bob on a string $3.00 \mathrm{~m}$ long is released with a velocity of $1.00 \mathrm{~m} / \mathrm{s}$ when the support string makes an angle of 30.0 degrees with the vertical. What is the tension in the string at the highest point of its motion?

A) $30.8 \mathrm{~N}$
B) $10.5 \mathrm{~N}$
C) $27.5 \mathrm{~N}$
D) $16.6 \mathrm{~N}$
E) $20.1 \mathrm{~N}$

Question 14

A $3.00 \mathrm{~kg}$ pendulum bob on a string $2.00 \mathrm{~m}$ long, is released with a velocity of $2.00 \mathrm{~m} / \mathrm{s}$ when the support string makes an angle of 45.0 degrees with the vertical. What is the tangential acceleration of the bob at the highest point of its motion?

A) $6.04 \mathrm{~m} / \mathrm{s}^{2}$
B) $7.80 \mathrm{~m} / \mathrm{s}^{2}$
C) $6.89 \mathrm{~m} / \mathrm{s}^{2}$
D) $8.20 \mathrm{~m} / \mathrm{s}^{2}$
E) $9.02 \mathrm{~m} / \mathrm{s}^{2}$

Question 15

A $2.00 \mathrm{~kg}$ pendulum bob on a string $2.00 \mathrm{~m}$ long, is released with a velocity of $1.50 \mathrm{~m} / \mathrm{s}$ when the support string makes an angle of 30.0 degrees with the vertical. What is the tangential acceleration of the bob at the highest point of its motion?

A) $6.25 \mathrm{~m} / \mathrm{s}^{2}$
B) $7.25 \mathrm{~m} / \mathrm{s}^{2}$
C) $5.33 \mathrm{~m} / \mathrm{s}^{2}$
D) $7.00 \mathrm{~m} / \mathrm{s}^{2}$
E) $5.77 \mathrm{~m} / \mathrm{s}^{2}$

Question 16

A $2.00 \mathrm{~kg}$ pendulum bob on a string $1.50 \mathrm{~m}$ long, is released with a velocity of $2.00 \mathrm{~m} / \mathrm{s}$ when the support string makes an angle of 30.0 degrees with the vertical. What is the speed of the bob at the bottom of the swing?

A) $4.32 \mathrm{~m} / \mathrm{s}$
B) $3.75 \mathrm{~m} / \mathrm{s}$
C) $3.04 \mathrm{~m} / \mathrm{s}$
D) $4.00 \mathrm{~m} / \mathrm{s}$
E) $2.82 \mathrm{~m} / \mathrm{s}$

Question 17

A $2.00 \mathrm{~kg}$ pendulum bob on a string $1.50 \mathrm{~m}$ long, is released with a velocity of $4.00 \mathrm{~m} / \mathrm{s}$ when the support string makes an angle of 30.0 degrees with the vertical. What is the angle with the vertical the bob makes at the highest point of its motion?

A) 56.7 degrees
B) 60.3 degrees
C) 45.0 degrees
D) 71.2 degrees
E) 85.3 degrees

Question 18

A $2.00 \mathrm{~kg}$ pendulum bob on a string $1.50 \mathrm{~m}$ long, is released with a velocity of $4.00 \mathrm{~m} / \mathrm{s}$ when the support string makes an angle of 30.0 degrees with the vertical. What is the speed of the bob at the bottom of the swing?

A) $4.47 \mathrm{~m} / \mathrm{s}$
B) $4.02 \mathrm{~m} / \mathrm{s}$
C) $3.75 \mathrm{~m} / \mathrm{s}$
D) $2.85 \mathrm{~m} / \mathrm{s}$
E) $3.50 \mathrm{~m} / \mathrm{s}$

Question 19

A $2.00 \mathrm{~kg}$ pendulum bob on a string $1.50 \mathrm{~m}$ long, is released with a velocity of $3.00 \mathrm{~m} / \mathrm{s}$ when the support string makes an angle of 45.0 degrees with the vertical. What is the angle with the vertical the bob makes at the highest point of its motion?

A) 50.0 degrees
B) 75.3 degrees
C) 66.4 degrees
D) 47.5 degrees
E) 59.8 degrees

Question 20

A $2.00 \mathrm{~kg}$ pendulum bob on a string $1.50 \mathrm{~m}$ long, is released with a velocity of $3.00 \mathrm{~m} / \mathrm{s}$ when the support string makes an angle of 45.0 degrees with the vertical. What is the tension in the string at the bottom of the swing?

A) $49.8 \mathrm{~N}$
B) $37.5 \mathrm{~N}$
C) $30.2 \mathrm{~N}$
D) $53.5 \mathrm{~N}$
E) $43.1 \mathrm{~N}$

Question 21

A $2.00 \mathrm{~kg}$ pendulum bob on a string $1.50 \mathrm{~m}$ long is released with a velocity of $0.00 \mathrm{~m} / \mathrm{s}$ when the support string makes an angle of 60.0 degrees with the vertical. What is the tension in the string at the bottom of the swing?

A) $50.1 \mathrm{~N}$
B) $55.6 \mathrm{~N}$
C) $42.6 \mathrm{~N}$
D) $39.2 \mathrm{~N}$
E) $60.4 \mathrm{~N}$

Question 22

A $75.0 \mathrm{~kg}$ skier, starting from rest, slides down a $75.0 \mathrm{~m}$ high slope without friction. The velocity of the skier at the bottom of the slope is

A) $40.5 \mathrm{~m} / \mathrm{s}$ .
B) $50.0 \mathrm{~m} / \mathrm{s}$ .
C) $20.6 \mathrm{~m} / \mathrm{s}$ .
D) $29.7 \mathrm{~m} / \mathrm{s}$ .
E) $38.3 \mathrm{~m} / \mathrm{s}$

Question 23

A student lifts a weight of $10.0 \mathrm{~N}$ a distance of 0.500 meters. The energy needed to do this work in calories is $(1 \mathrm{cal}=4.186$ Joules)

A) $1.19 \mathrm{cal}$ .
B) $2.30 \mathrm{cal}$ .
C) $0.570 \mathrm{cal}$ .
D) $0.750 \mathrm{cal}$ .
E) $1.75 \mathrm{cal}$ .

Question 24

An $8000 \mathrm{~kg}$ satellite is launched from the surface of the Earth and injected into a circular orbit at an altitude of $100 \mathrm{~km}$ above the surface of the Earth. The gravitational potential energy of the satellite in the circular orbit is $\left(\mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}, \mathrm{M}_{\mathrm{E}}=5.97 \times 10^{24} \mathrm{~kg}, \mathrm{R}_{\mathrm{E}}=6.37 \times 10^{6} \mathrm{~m}\right)$

A) $-5.01 \times 1011 \mathrm{~J}$ .
B) $-4.75 \times 1011 \mathrm{~J}$ .
C) $-4.02 \times 1011 \mathrm{~J}$ .
D) $-4.92 \times 1011 \mathrm{~J}$ .
E) $-3.85 \times 1011 \mathrm{~J}$

Question 25

An $8000 \mathrm{~kg}$ satellite is launched from the surface of the Earth and injected into a circular orbit at an altitude of $100 \mathrm{~km}$ above the surface of the Earth. The kinetic energy of the satellite in the circular orbit is $(G=6.67 \times$ $10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}, \mathrm{M}_{\mathrm{E}}=5.97 \times 1024 \mathrm{~kg}, \mathrm{R}_{\mathrm{E}}=6.37 \times 10^{6} \mathrm{~m}$ )

A) $5.02 \times 1011 \mathrm{~J}$ .
B) $3.45 \times 1011 \mathrm{~J}$ .
C) $2.01 \times 1011 \mathrm{~J}$ .
D) $4.25 \times 1011 \mathrm{~J}$ .
E) $2.46 \times 10^{11} \mathrm{~J}$ .

Question 26

An $8000 \mathrm{~kg}$ satellite is launched from the surface of the Earth into outer space. What initial kinetic energy is needed by the satellite in order to reach a great (i.e., infinite) distance from the Earth, neglecting the effects of air resistance in the atmosphere? $\left(\mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}, \mathrm{M}_{\mathrm{E}}=5.97 \times 10^{24} \mathrm{~kg}, \mathrm{R}_{\mathrm{E}}=6.37 \times 10^{6} \mathrm{~m}\right.$ .)

A) $5.00 \times 1011 \mathrm{~J}$ .
B) $3.00 \times 1011 \mathrm{~J}$ .
C) $2.35 \times 1011 \mathrm{~J}$ .
D) $4.03 \times 1011 \mathrm{~J}$ .
E) $3.57 \times 1011 \mathrm{~J}$ .

Question 27

The graph shows the force on an object as it moves a distance $\mathrm{x}$ . What is the work done by the force as the object moves from $0.0 \mathrm{~m}$ to $10.0 \mathrm{~m}$ ?

A) $52 \mathrm{~J}$
B) $75 \mathrm{~J}$
C) $34 \mathrm{~J}$
D) $45 \mathrm{~J}$
E) $64 \mathrm{~J}$

Question 28

The graph shows the force on an object as it moves a distance $\mathrm{x}$ . What is the work done by the force as the object moves from $0.0 \mathrm{~m}$ to $4.0 \mathrm{~m}$ ?

A) $10 \mathrm{~J}$
B) $6.0 \mathrm{~J}$
C) $8.0 \mathrm{~J}$
D) $14 \mathrm{~J}$
E) $12 \mathrm{~J}$

Question 29

A spring is stretched from $0.500 \mathrm{~m}$ to $0.800 \mathrm{~m}$ . Assume the unstretched position is $0.00 \mathrm{~m}$ . If the spring constant of the spring is $10.0 \mathrm{~N} / \mathrm{m}$ , what is the work done on the spring?

A) $3.01 \mathrm{~J}$
B) $1.95 \mathrm{~J}$
C) $2.21 \mathrm{~J}$
D) $2.45 \mathrm{~J}$
E) $2.75 \mathrm{~J}$

Question 30

A car has a mass of 2,000 kg and travels at $20.0 \mathrm{~m} / \mathrm{s}$ . If the drag force is $100 \mathrm{~N}$ , then the power the engines have to provide to keep moving at constant speed is

A) $3.9 \mathrm{~kW}$ .
B) $2.0 \mathrm{~kW}$ .
C) $4.2 \mathrm{~kW}$ .
D) $2.9 \mathrm{~kW}$ .
E) $3.4 \mathrm{~kW}$ .

Question 31

During a basketball game, a player shoots a ball from half-court. When the ball reaches its maximum height of $4.5 \mathrm{~m}$ above the floor, it is moving at $5.0 \mathrm{~m} / \mathrm{s}$ . If the ball was released from $2.5 \mathrm{~m}$ above the floor, what was the angle above the horizontal of the ball's initial velocity?

A) $58^{\circ}$
B) $54^{\circ}$
C) $39^{\circ}$
D) $51^{\circ}$
E) $32^{\circ}$
F) $36^{\circ}$

Question 32

An asteroid of mass $1.4 \times 10^{14} \mathrm{~kg}$ is observed to have an escape speed equal to a typical person's maximum jumping speed, $3.0 \mathrm{~m} / \mathrm{s}$ . What is its radius?

A) $1.0 \mathrm{~km}$
B) $0.5 \mathrm{~km}$
C) $2.1 \mathrm{~km}$
D) $6.3 \mathrm{~km}$

Question 33

An asteroid of radius $2.1 \mathrm{~km}$ is observed to have an escape speed equal to a typical person's maximum jumping speed, $3.0 \mathrm{~m} / \mathrm{s}$ . What is its mass?

A) $2.8 \times 1014 \mathrm{~kg}$
B) $4.2 \times 1014 \mathrm{~kg}$
C) $0.5 \times 1014 \mathrm{~kg}$
D) $1.4 \times 1014 \mathrm{~kg}$
E) $5.7 \times 10^{14} \mathrm{~kg}$

Question 34

A comet is observed to pass $1.50 \times 10^{8} \mathrm{~m}$ from the surface of the Sun. The Sun's radius is $6.96 \times 10^{8}$ $\mathrm{m}$ . What is the speed of the comet at this point, if its speed when passing the Earth's orbit, $1.50 \times 10^{11} \mathrm{~m}$ from the Sun's center, is $25 \mathrm{~km} / \mathrm{s}$ ? $\left(\mathrm{M}_{\mathrm{S}}=1.989 \times 10^{30} \mathrm{~kg}\right.$ . $)$

A) $562 \mathrm{~km} / \mathrm{s}$
B) $585 \mathrm{~km} / \mathrm{s}$
C) $618 \mathrm{~km} / \mathrm{s}$
D) $559 \mathrm{~km} / \mathrm{s}$

Question 35

An $0.10 \mathrm{~g}$ flea, having leapt from the surface of a dog's cranium, is observed to be moving at $1.25 \mathrm{~m} / \mathrm{s}$ when it is $5.00 \mathrm{~cm}$ above the position from which it leapt. What was the elastic potential energy stored in its legs before its leap?

A) $4.9 \times 10^{-5} \mathrm{~J}$
B) $5.7 \times 10^{-3} \mathrm{~J}$
C) $1.3 \times 10^{-4} \mathrm{~J}$
D) $5.7 \times 10^{-4} \mathrm{~J}$
E) $1.3 \times 10^{-3} \mathrm{~J}$
F) $7.8 \times 10^{-5} \mathrm{~J}$