Deck 6: Conservation of Energy

Question 1

A 20 N horizontal force is applied to a 4.0 kg box. Friction is negligible. The box moves a horizontal distance of 3.0 meters. The work done by the 20 N force is

A) 60 J.
B) 80 J.
C) 10 J.
D) 92 J.
E) 65 J.

Answer 1

60 J.

Question 2

A 20.0 kg box slides down a 12.0 m long incline at an angle of 3.0 degrees with the horizontal. A force of 50.0 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) 300 J.
B) 372 J.
C) 410 J.
D) 455 J.
E) 525 J.

Answer 2

372 J.

Question 3

A 20.0 kg box slides up a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 150 N is applied to the box to pull it up 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) 330 J.
B) 390 J.
C) 420 J.
D) 481 J.
E) 597 J.

Answer 3

420 J.

Question 4

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

A) 75.0 J.
B) 61.3 J.
C) 50.1 J.
D) 46.3 J.
E) 40.5 J.

Question 5

A 20.0 kg box slides up a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 150 N is applied to the box to pull it up the incline. The applied force makes an angle of 10.0 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) 424 J.
B) 395 J.
C) 344 J.
D) 297 J.
E) 250 J.

Question 6

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

A) 4,500 N.
B) 4,200 N.
C) 3,750 N.
D) 3,000 N.
E) 2,400 N.

Question 7

A 20.0 kg box slides down a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 50.0 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 J.
B) 475 J.
C) 521 J.
D) 585 J.
E) 620 J.

Question 8

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 m to 8.0 m?

A) 35 J
B) 48 J
C) 50 J
D) 52 J
E) 60 J

Question 9

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

A) 22.0 J.
B) 26.5 J.
C) 30.3 J.
D) 35.2 J.
E) 40.7 J.

Question 10

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 0.0 m to 6.0 m?

A) 14 J
B) 12 J
C) 10 J
D) 8.0 J
E) 6.0 J

Question 11

A horizontal force of 12 newtons is applied to a 4.0 kg box that slides on a horizontal surface. The box starts from rest, moves a horizontal distance of 10 meters, and obtains a velocity of 5.0 m/s. The surface has friction. The friction force, assumed constant, is

A) 7.0 N.
B) 6.5 N.
C) 6.0 N.
D) 5.7 N.
E) 4.9 N.

Question 12

The explosion in a cannon exerts an average force of 30,000 N for 2.00 meters. The velocity of a 2.00 kg projectile shot from the cannon is

A) 198 m/s.
B) 245 m/s.
C) 302 m/s.
D) 354 m/s.
E) 412 m/s.

Question 13

A car traveling at 30 mph skids to a stop in 60 meters. If an identical car traveling at 60 mph skids to a stop under the same conditions, what distance would it travel?

A) 340 m
B) 310 m
C) 260 m
D) 240 m
E) 190 m

Question 14

The explosion in a cannon exerts an average force of 30,000 N for L meters, the length of the cannon. What length of the cannon would be necessary to shoot a 2.0 kg projectile from the surface of the Earth to a distance of 6.84 × 10⁸ m from the center of the Earth (the same as the distance to the Moon)? (G = 6.67 × 10⁻¹¹ N·m²/kg², ME = 5.97 × 10²⁴ kg, and RE = 6.37 × 10⁶ m.)

A) 2.7 km.
B) 3.0 km.
C) 3.9 km.
D) 4.1 km.
E) 5.0 km.

Question 15

The most fundamental forms of energy are

A) elastic, gravitational, internal.
B) kinetic, potential, rest.
C) electromagnetic, chemical, nuclear.
D) translational, rotational, vibrational.

Question 16

A 20.0 kg box slides down a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 50.0 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) 203 J.
B) 275 J.
C) 300 J.
D) 392 J.
E) 425 J.

Question 17

A 5.00 gram bullet has a velocity of 300 m/s. It strikes a block of wood and penetrates to a depth of 10.0 cm. The average force of the block of wood on the bullet is

A) 1,500 N.
B) 1,750 N.
C) 1,870 N.
D) 2,030 N.
E) 2,250 N.

Question 18

A 20.0 kg box slides down a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 50.0 N is applied to the box in the upward direction. The applied force F makes an angle of 0.00 to the incline. If the incline is frictionless, then the increase in the kinetic energy of the box is

A) 620 J.
B) 576 J.
C) 542 J.
D) 500 J.
E) 475 J.

Question 19

A 30.00 kg box slides up a 12.00 meter long incline at an angle of 30.00 degrees above the horizontal. Friction is negligible. The change in gravitational potential energy is

A) 2110 J.
B) 1467 J.
C) 1080 J.
D) 1764 J.
E) 760.0 J.

Question 20

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

A) 9,340 N.
B) 11,250 N.
C) 15,200 N.
D) 19,500 N.
E) 21,400 N.

Question 21

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

A) 3.10 × 10⁶ J.
B) 2.56 × 10⁶ J.
C) 2.01 × 10⁶ J.
D) 1.85 × 10⁶ J.
E) 1.13 × 10⁶ J.

Question 22

In order to conserve fuel, you modify your car by removing 100 kg of excess weight. How much energy is saved each time you accelerate from 0 to 100 km/hr (62 mph)?

A) 2.86 × 10² J
B) 2.86 × 10⁴ J
C) 3.86 × 10⁴ J
D) 3.86 × 10² J

Question 23

A 2.00 kg pendulum bob on a string 1.50 m long, is released with a velocity of 4.00 m/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 m/s
B) 4.02 m/s
C) 3.75 m/s
D) 3.50 m/s
E) 2.85 m/s

Question 24

A 3.00 kg pendulum bob on a string 2.00 m long, is released with a velocity of 2.00 m/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 m/s²
B) 6.89 m/s²
C) 7.80 m/s²
D) 8.20 m/s²
E) 9.02 m/s²

Question 25

A 20.0 kg box slides up a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 150 N is applied to the box to pull it up the incline. The applied force makes an angle of 10.0 degrees to the incline. What is the change in gravitational potential energy of the box?

A) 2,570 J
B) 2,350 J
C) 1,450 J
D) 1,180 J
E) 945 J

Question 26

A horizontal force is applied to a 2.0 kg box. The box starts from rest, moves a horizontal distance of 12.0 meters, and obtains a velocity of 8.0 m/s. The change in the kinetic energy is

A) 32 J.
B) 48 J.
C) 50 J.
D) 58 J.
E) 64 J.

Question 27

As a hiker descends a hill, the work done by gravity on the hiker is

A) positive and depends on the path taken.
B) negative and depends on the path taken.
C) positive and independent of the path taken.
D) negative and independent of the path taken.

Question 28

A 3.00 kg pendulum bob on a string 2.00 m long is released with a velocity of 2.00 m/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) 12.5 N
B) 17.8 N
C) 21.4 N
D) 28.9 N
E) 31.6 N

Question 29

A 2.00 kg pendulum bob on a string 1.50 m long is released with a velocity of 0.00 m/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) 60.4 N
B) 55.6 N
C) 50.1 N
D) 42.6 N
E) 39.2 N

Question 30

A 2.00 kg pendulum bob on a string 2.00 m long, is released with a velocity of 1.50 m/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) 5.33 m/s²
B) 5.77 m/s²
C) 6.25 m/s²
D) 7.00 m/s²
E) 7.25 m/s²

Question 31

A 120 N force is applied at an angle of 30.0 degrees above the horizontal to a 4.00 kg box on a frictionless surface. The box moves a horizontal distance of 8.00 meters. The change in the kinetic energy of the box is

A) 667 J.
B) 750 J.
C) 831 J.
D) 890 J.
E) 920 J.

Question 32

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

A) 20.6 m/s.
B) 29.7 m/s.
C) 38.3 m/s.
D) 40.5 m/s.
E) 50.0 m/s.

Question 33

A 2.00 kg pendulum bob on a string 1.50 m long, is released with a velocity of 4.00 m/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) 85.3 degrees
B) 71.2 degrees
C) 60.3 degrees
D) 56.7 degrees
E) 45.0 degrees

Question 34

A 2000 kg car accelerates from rest to a velocity of 40 m/s in 5.0 seconds. The brakes are applied, and the car is brought to a stop (without sliding). The magnitude of the work done by the friction in the brakes is

A) 1.0 × 10⁶ J.
B) 1.2 × 10⁶ J.
C) 1.6 × 10⁶ J.
D) 2.1 × 10⁶ J.
E) 2.5 × 10⁶ J.

Question 35

A 5.00 kg box slides up a 10.0 m long incline at an angle of 20.0 degrees with the horizontal, pushed by a 40.0 N force parallel to the incline. The coefficient of kinetic friction is 0.100. The change in kinetic energy is

A) 105 J.
B) 145 J.
C) 186 J.
D) 200 J.
E) 243 J.

Question 36

A 2.00 kg pendulum bob on a string 1.50 m long, is released with a velocity of 2.00 m/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 m/s
B) 4.00 m/s
C) 3.75 m/s
D) 3.04 m/s
E) 2.82 m/s

Question 37

A 120 N horizontal force is applied to a 4.00 kg box on a frictionless surface. The box moves a horizontal distance of 8.00 meters. The change in the kinetic energy of the box is

A) 960 J.
B) 875 J.
C) 821 J.
D) 765 J.
E) 633 J.

Question 38

A 2.00 kg pendulum bob on a string 3.00 m long is released with a velocity of 1.00 m/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 N
B) 27.5 N
C) 20.1 N
D) 16.6 N
E) 10.5 N

Question 39

A 2.00 kg pendulum bob on a string 1.50 m long, is released with a velocity of 3.00 m/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) 47.5 degrees
B) 50.0 degrees
C) 59.8 degrees
D) 66.4 degrees
E) 75.3 degrees

Question 40

A 2.00 kg pendulum bob on a string 1.50 m long, is released with a velocity of 3.00 m/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) 53.5 N
B) 49.8 N
C) 43.1 N
D) 37.5 N
E) 30.2 N

Question 41

In order to conserve fuel, you modify your car by removing 100 kg of excess weight. How much energy is saved each time you drive up a 3 km high mountain?

A) 2.94 × 10⁶ J
B) 2.86 × 10⁴ J
C) 3.86 × 10⁶ J
D) 3.00 × 10⁵ J

Question 42

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 0.0 m to 4.0 m?

A) 6.0 J
B) 8.0 J
C) 10 J
D) 12 J
E) 14 J

Question 43

An 8000 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? (G = 6.67 × 10⁻¹¹ N·m²/kg², M_E = 5.97 × 10²⁴ kg, R_E = 6.37 × 10⁶ m.)

A) 5.00 × 10¹¹ J.
B) 4.03 × 10¹¹ J.
C) 3.57 × 10¹¹ J.
D) 3.00 × 10¹¹ J.
E) 2.35 × 10¹¹ J.

Question 44

A 200 N box is pushed at a constant velocity up an incline that is 5.00 m long and rises 1.00 m. The incline has a coefficient of kinetic friction of 0.200, and the pushing force is parallel to the incline. The work done by the pushing force is

A) 475 J.
B) 422 J.
C) 356 J.
D) 300 J.
E) 396 J.

Question 45

A spring-powered dart gun is unstretched and has a spring constant 16.0 N/m. The spring is compressed by 8.0 cm and a 5.0 gram projectile is placed in the gun. The kinetic energy of the projectile when it is shot from the gun is

A) 0.125 J.
B) 0.090 J.
C) 0.075 J.
D) 0.051 J.
E) 0.030 J.

Question 46

An 8000 kg satellite is launched from the surface of the Earth into outer space. What initial speed 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? (G = 6.67 × 10⁻¹¹ N·m²/kg², M_E = 5.97 × 10²⁴ kg, R_E = 6.37 × 10⁶ m.)

A) 8,450 m/s.
B) 9,200 m/s.
C) 11,180 m/s.
D) 18,900 m/s.
E) 25,200 m/s.

Question 47

A spring-powered dart gun is unstretched and has a spring constant 100 N/m. The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun. The maximum height of the projectile when it is shot straight up from the gun is

A) 7.57 m.
B) 7.00 m.
C) 6.53 m.
D) 6.00 m.
E) 5.50 m.

Question 48

A spring with a spring constant of 8.0 N/m is compressed to 20 cm. If the spring was uncompressed initially, then the work done (by the compressing force) is

A) 0.12 J.
B) 0.16 J.
C) 0.19 J.
D) 0.22 J.
E) 0.26 J.

Question 49

A 1 kg mass is attached to a vertical spring, stretching it by 10 cm from its equilibrium position. With the spring secured in the same stretched position, the 1 kg mass is removed and replaced with a 0.50 kg mass. If the spring is then released, how high will the 0.50 kg mass rise above the point where it was released?

A) 0.10 m
B) 0.24 m
C) 0.44 m
D) 0.80 m
E) 1.0 m

Question 50

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

A) 1.95 J
B) 2.21 J
C) 2.45 J
D) 2.75 J
E) 3.01 J

Question 51

An 8000 kg satellite is launched from the surface of the Earth and injected into a circular orbit at an altitude of 100 km above the surface of the Earth. The gravitational potential energy of the satellite in the circular orbit is (G = 6.67 × 10⁻¹¹ N·m²/kg², M_E = 5.97 × 10²⁴ kg, R_E = 6.37 × 10⁶ m)

A) −5.01 × 10¹¹ J.
B) −4.92 × 10¹¹ J.
C) −4.75 × 10¹¹ J.
D) −4.02 × 10¹¹ J.
E) −3.85 × 10¹¹ J.

Question 52

A 200 N box is pushed at a constant velocity up an incline that is 5.00 m long and rises 1 m. If the incline is frictionless, then the work done by the pushing force is

A) 336 J.
B) 305 J.
C) 275 J.
D) 200 J.
E) 157 J.

Question 53

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

A) 0.570 cal.
B) 0.750 cal.
C) 1.19 cal.
D) 1.75 cal.
E) 2.30 cal.

Question 54

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 0.0 m to 10.0 m?

A) 34 J
B) 45 J
C) 52 J
D) 64 J
E) 75 J

Question 55

A spring-powered dart gun is unstretched and has a spring constant 16.0 N/m. The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun. The velocity of the projectile when it is shot from the gun is

A) 2.04 m/s.
B) 2.75 m/s.
C) 3.50 m/s.
D) 3.75 m/s
E) 4.53 m/s.

Question 56

An 8000 kg satellite is launched from the surface of the Earth and injected into a circular orbit at an altitude of 100 km above the surface of the Earth. The kinetic energy of the satellite in the circular orbit is (G = 6.67 × 10⁻¹¹ N·m²/kg², M_E = 5.97 × 1024 kg, R_E = 6.37 × 10⁶ m)

A) 5.02 × 10¹¹ J.
B) 4.25 × 10¹¹ J.
C) 3.45 × 10¹¹ J.
D) 2.46 × 10¹¹ J.
E) 2.01 × 10¹¹ J.

Question 57

A spring with a spring constant of 8.0 N/m is initially compressed to 5.0 cm. The work done (by the external force) as it is compressed another 15 cm, to a total compression of 20 cm, is

A) 0.85 J.
B) 0.54 J.
C) 0.25 J.
D) 0.15 J.
E) 0.09 J.

Question 58

A spring-powered dart gun is unstretched and has a spring constant 12.0 N/m. The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun. The velocity of the projectile when it is shot from the gun is

A) 1.52 m/s.
B) 2.54 m/s.
C) 3.92 m/s.
D) 4.24 m/s.
E) 5.02 m/s.

Question 59

A 20.0 kg box slides up a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 150 N is applied to the box to pull it up the incline. The applied force makes an angle of 10.0 degrees to the incline. What is the work done by the applied force?

A) 1,870 J
B) 1,770 J
C) 1,500 J
D) 1,450 J
E) 1,380 J

Question 60

A spring-powered dart gun is unstretched and has a spring constant 150 N/m. The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun. The maximum height of the projectile when it is shot at an angle of 30.0 degrees above the horizontal from the gun is

A) 5.03 m.
B) 4.24 m.
C) 3.90 m.
D) 3.20 m.
E) 2.45 m.

Question 61

A comet is observed to pass 1.50 × 10⁸ m from the surface of the Sun. The Sun's radius is 6.96 × 10⁸ m. What is the speed of the comet at this point, if its speed when passing the Earth's orbit, 1.50 × 10¹¹ m from the Sun's center, is 25 km/s? (M_S = 1.989 × 10³⁰ kg.)

A) 559 km/s
B) 618 km/s
C) 562 km/s
D) 585 km/s

Question 62

A 90.0 kg person is running up some stairs at 0.500 m/s. If the staircase is angled at 45.0° to the horizontal, then the power needed to run up the stairs is

A) 312 Watts.
B) 395 Watts.
C) 302 Watts.
D) 275 Watts.
E) 441 Watts.

Question 63

During a basketball game, a player shoots a ball from half-court. When the ball reaches a height of 4.5 m above the floor, it is moving at 5.0 m/s. Assuming the shot was perfectly made, it will pass through the rim of the basket, 3.05 m above the floor. How fast is the ball moving when it passes through the rim?

A) 7.7 m/s
B) 7.3 m/s
C) 9.2 m/s
D) 5.3 m/s

Question 64

A 1.1 kg seagull takes off from a piling along the California coast and accelerates in 0.50 s to a flight speed of 7.5 m/s. The seagull flies along a slightly inclined path, such that at the end of the 0.50 s period, it is 5.3 m above its point of takeoff. What average power is delivered by the bird's wings during the takeoff?

A) 180 W
B) 110 W
C) 52 W
D) 62 W

Question 65

When the escape speed from the surface of a spherical object of mass M and radius R is equal to the speed of light, that radius is called the Schwarzschild radius for the given mass. What is the Schwarzschild radius of the Sun, whose mass is 2.0 × 10³⁰ kg? (i.e., if all the Sun's mass were compressed into a sphere of this radius, the escape speed from its surface would be the speed of light-it would become a black hole!)

A) 4.5 km
B) 1.5 km
C) 5.9 km
D) 3.0 km

Question 66

A blob of clay of mass M is propelled upward from a spring that is initially compressed by an amount d. The spring constant is k. What is the ultimate height h above the unstretched spring's end that the clay will reach?

A) kd²/(Mg)
B) kd^{2/(2Mg) − d}
C) kd^{2/(Mg) − d}
D) kd^2/(2Mg)

Question 67

A 1.1 kg seagull takes off from a piling along the California coast and accelerates in 0.50 s to a flight speed of 7.5 m/s. Assuming the seagull flies along a horizontal path (at the same height as its takeoff), what average power is delivered by the bird's wings during the takeoff?

A) 62 W
B) 8.3 W
C) 33 W
D) 250 W

Question 68

A blob of clay of mass M is dropped onto a spring from a height h above the end of the spring. If the spring compresses by an amount d as the blob comes to rest, what is the spring constant k?

A) 2Mgh/d²
B) Mgh/d²
C) Mg(h+d)/d²
D) 2Mg(h+d)/d²

Question 69

An airplane has a mass of 30,000 kg and travels at 300 m/s. If the drag force is 1000 N, then the power the engines have to provide to keep flying at a constant speed is

A) 6.0 × 10⁵ W.
B) 5.5 × 10⁵ W.
C) 4.9 × 10⁵ W.
D) 4.2 × 10⁵ W.
E) 3.0 × 10⁵ W.

Question 70

A spring-powered dart gun is unstretched and has a spring constant 10.0 N/m. The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun. The kinetic energy of the projectile when it is shot from the gun is

A) 0.020 J.
B) 0.032 J.
C) 0.060 J.
D) 0.100 J.
E) 0.120 J.

Question 71

A 1800 kg car moving at 20 m/s hits an initially uncompressed spring with a spring constant of 2.0 × 10⁶ N/m. The maximum compression of the spring is

A) 0.40 m.
B) 0.60 m.
C) 0.80 m.
D) 1.0 m.
E) 1.2 m.

Question 72

A ski lift carries passengers up a 150 m high slope at the rate of one chair every 30.0 seconds. If the chair will hold two passengers with a combined total mass of 190 kg, then the power output of the engine that powers the ski lift is

A) 6.96 kW.
B) 7.83 kW.
C) 8.75 kW.
D) 9.31 kW.
E) 9.90 kW.

Question 73

A dragster drives a quarter mile (402 m) at a constant rate of acceleration, starting from rest and finishing the race with a final speed of 450 km/hr. The mass of the dragster, together with its driver, is 975 kg. What average power is provided by the engine, if 50% of the power output is delivered to the wheels? Neglect dissipative forces.

A) 4.7 MW
B) 1.2 MW
C) 0.6 MW
D) 2.4 MW

Question 74

A student lifts a weight of 10.0 N a distance of 0.5 meters. If this exercise is repeated 50 times in 100 seconds, then the average power output of the student is

A) 2.5 W.
B) 3.1 W.
C) 3.6 W.
D) 4.0 W.
E) 4.8 W.

Question 75

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

A) 2.0 kW.
B) 2.9 kW.
C) 3.4 kW.
D) 3.9 kW.
E) 4.2 kW.

Question 76

A 2500 kg car accelerates from rest to a velocity of 10 m/s in 5.0 seconds. The average power of the engine during this acceleration is

A) 50 kW.
B) 47 kW.
C) 40 kW.
D) 31 kW.
E) 25 kW.

Question 77

An asteroid of mass 1.4 × 10¹⁴ kg is observed to have an escape speed equal to a typical person's maximum jumping speed, 3.0 m/s. What is its radius?

A) 6.3 km
B) 2.1 km
C) 1.0 km
D) 0.5 km

Question 78

A road bicycle racer rides down the highway from Pike's peak. During one stretch of the ride, he descends 150 m while accelerating from 35 km/hr to some final speed. Assuming friction and air resistance to be negligible, and treating kinetic energy as purely translational (i.e., ignoring any rotational part), what is his final speed?

A) 113 km/h
B) 198 km/h
C) 148 km/h
D) 169 km/h

Question 79

A 2000 kg car accelerates from rest to a velocity of 20 m/s in 10 seconds. The average power of the engine during this acceleration is

A) 50 kW.
B) 40 kW.
C) 30 kW.
D) 20 kW.
E) 10 kW.

Question 80

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

A) 4.2 × 10¹⁴ kg
B) 2.8 × 10¹⁴ kg
C) 5.7 × 10¹⁴ kg
D) 0.5 × 10¹⁴ kg
E) 1.4 × 10¹⁴ kg