Deck 5: Work and Energy

Question 1

Define mechanical work.

Answer 1

Mechanically, work involves force and displacement, work is used to describe quantitatively what is accomplished when a force acts on an object as it moves through a distance.

Question 2

State the law of the conservation of mechanical energy.

Answer 2

In a conservative system, the sum of all types of kinetic energy and potential energy is constant and equals the total mechanical energy of the system.

Question 3

What distinguishes work done by conservative versus nonconservative forces?

Answer 3

Work done by a conservative force is independent of the object's path and the work only depends upon the initial and final positions. Work done by nonconservative forces is path dependent.

Question 4

Define power.

Question 5

Describe mechanical efficiency.

Question 6

Problems involving a non-conservative force cannot be solved because there is no definable potential energy.

Question 7

Which of the following is not a unit of work?

A) Kw-h
B) Kg-m/s
C) N-m
D) J
E) W-s

Question 8

The area under the curve, on a Force-position (F-x) graph, represents

A) work.
B) kinetic energy.
C) power.
D) friction.
E) efficiency.

Question 9

Work done by STATIC FRICTION is always

A) positive.
B) perpendicular to the surface.
C) along the surface.
D) negative.
E) zero.

Question 10

You throw a ball straight up. Compare the sign of the work done by gravity while the ball goes up with the sign of the work done by gravity while it goes down.

A) Work up is +, and the work down is -.
B) Work up is -, and the work down is -.
C) Work up is +, and the work down is +.
D) Work up is -, and the work down is +.

Question 11

On a plot of F vs. x, what represents the work done by the force F?

A) the length of the curve
B) the slope of the curve
C) the maximum F times minimum x
D) the product of the maximum force times the maximum x
E) the area under the curve

Question 12

Consider an ideal elastic spring. The spring constant is

A) proportional to the mass attached to the spring.
B) proportional to displacement from equilibrium.
C) inversely proportional to the displacement.
D) inversely proportional to the applied force.
E) none of the other answers.

Question 13

Use Figure 5-1 below to answer the following question(s).


-Which of the graphs above illustrates Hooke's Law?

A) graph a
B) graph b
C) graph c
D) graph d
E) none of the above

Question 14

The work energy theorem says

A) the net work done plus the initial kinetic energy is the final kinetic energy.
B) final kinetic energy plus the net work done is the initial kinetic energy.
C) the net work done plus the final kinetic energy is the initial kinetic energy.
D) the net work done minus the initial kinetic energy is the final kinetic energy.
E) the net work done is equal to the initial kinetic energy less the final energy.

Question 15

Car J moves twice as fast as car K, and car J has half the mass of car K. The kinetic energy of car J, compared to car K is

A) 1 to 2.
B) 2 to 1.
C) the same.
D) 4 to 1.
E) 4² to 1.

Question 16

If both the mass and the velocity of a ball are tripled, the kinetic energy is increased by a factor of

A) 6.
B) 9.
C) 18.
D) 81.
E) 27.

Question 17

A truck weighs twice as much as a car, and is moving at twice the speed of the car. Which statement is true about the truck's kinetic energy (K) compared to that of the car?

A) The truck has 4 times the K of the car.
B) The truck has 8 times the K of the car.
C) The truck has twice the K of the car.
D) All that can be said is that the truck has more K.
E) The truck has times the K of the car.

Question 18

A 200-g mass attached to the end of a spring causes it to stretch 5.0 cm. If another 200-g mass is added to the spring, the potential energy of the spring will be

A) 4 times as much.
B) the same.
C) times as much.
D) twice as much.
E) 3 times as much.

Question 19

A leaf falls from a tree. Compare its kinetic energy K to its potential energy U.

A) K decreases, and U decreases.
B) K and U remain constant.
C) K increases, and U increases.
D) K decreases, and U increases.
E) K increases, and U decreases.

Question 20

The total mechanical energy of a system

A) is either all kinetic energy or all potential energy, at any one instant.
B) can never be negative.
C) is equally divided between kinetic energy and potential energy.
D) is constant only if nonconservative forces act.
E) is constant only if conservative forces act.

Question 21

Use Figure 5-2 below to answer the following question(s).


-In Figure 5-2, showing a pendulum, at what position is the potential energy maximum?

A) A
B) B
C) C

Question 22

Use Figure 5-2 below to answer the following question(s).


-In Figure 5-2, showing a pendulum, at what position is the kinetic energy maximum?

A) A
B) B
C) C

Question 23

A ball is released, from rest, at the left side of the loop-the-loop, at the height, h, as shown in Figure 5-3.


-Refer to Figure 5-3. If the radius of the loop is R, what minimum height h allows the ball not to fall off the track at the top of the loop?

A) 3.5 R
B) R
C) 2.5 R
D) 2.0 R
E) 3.0 R

Question 24

A ball is released, from rest, at the left side of the loop-the-loop, at the height, h, as shown in Figure 5-3.


-Refer to Figure 5-3. If the radius of the loop is R, what vertical height does the ball rise to, on the other side, neglecting friction?

A) 2R
B) greater than 2R
C) R
D) less than R

Question 25

You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fast, what distance would the car have skidded, under the same conditions?

A) It would have skidded half as far.
B) It would have skidded 4 times farther.
C) It would have skidded twice as far.
D) It is impossible to tell from the information given.
E) It would have skidded times farther.

Question 26

A 4-kg mass moving with speed 2 m/s, and a 2-kg mass moving with a speed of 4 m/s, are gliding over a horizontal frictionless surface. Both objects encounter the same horizontal force, which directly opposes their motion, and are brought to rest by it. Which statement correctly describes the situation?

A) Both masses travel the same distance before stopping.
B) The 2-kg mass travels farther, but not necessarily twice as far.
C) The 2-kg mass travels twice as far as the 4-kg mass before stopping.
D) The 4-kg mass loses more kinetic energy than the 2-kg mass.
E) The 4-kg mass travels twice as far as the 2-kg mass before stopping.

Question 27

A horse-power is equal to 550

A) ft-lb/s.
B) J/hour.
C) Kw-h.
D) J/s.
E) ft-lb/minute.

Question 28

To accelerate your car at a constant acceleration, the car's engine must

A) maintain a constant turning speed.
B) maintain a constant power output.
C) develop ever-increasing power.
D) develop ever-decreasing power.

Question 29

An auto is coasting on a level road. It weighs 10. kN. How much work is done by gravity as it moves horizontally 150. meters?

Question 30

Is more work required to increase a car's speed from rest to 30 mph, or from 50 mph to 60 mph?

Question 31

A driver, traveling at 22. m/s, slows down her 1500. kg car to stop for a red light. What work is done by the friction force against the wheels?

Question 32

A cyclist does work at the rate of 500. W while riding. With how much average horizontal force does the wheel push when she is traveling at 10. m/s?

Question 33

A simple pendulum, with a 4.4 kg mass and length 75. cm, is released from rest at an angle of 50.°
(a) To what height does the mass swing on the other side?
(b) What is the speed of the mass at the bottom of the swing?

Question 34

Assuming muscles are 20% efficient, at what rate is a 60. kg boy using energy when he runs up a flight of stairs 10. m high, in 8.0 s?

Question 35

A roofer lifts supplies a height of 20. m with a hand-operated winch. How long would it take him to lift a 200. kg load, if the winch has an efficiency of 90%, and the rate at which the winch can do work is 0.80 hp?

Question 36

A family goes on vacation for one week, but forgets to turn off an electric fan that consumes electricity at the rate of 200 watts. If the cost of electricity is $0.120/kW-h, how much does it cost to run the fan?

Question 37

When you lift a 12. ounce beverage can from the table top to your mouth, you do approximately how much work?

A) 1 Calorie
B) 1 erg
C) 1 Watt
D) 1 Kw-h
E) 1 Joule

Question 38

Matthew pulls his little sister Sarah in a sled on an icy surface (assume no friction), with a force of 60.0 Newtons at an angle of 37.0° upward from the horizontal. If he pulls her a distance of 12.0 m, the work he does is

A) 720 J
B) 185 J
C) 575 J
D) 0.333 kJ
E) 433 J

Question 39

A 4.0 kg box of fruit slides 8.0 m down a ramp, inclined at 30.° from the horizontal. If the box slides at a constant velocity of 5.0 m/s, the work done by gravity is

A) 0.16 kJ.
B) -0.16 kJ.
C) -78. J.
D) zero.
E) +78. J.

Question 40

A container of water is lifted vertically 3.0 m, then returned to its original position. If the total weight is 30. N, how much work was done?

A) No work was done.
B) 90 J
C) 45 J
D) 0.18 kJ
E) 0.90 kJ

Question 41

-The force that a squirrel exerts on a nut it has found is observed over a 10. second interval, as shown in Figure 5-4. How much work did the squirrel do during that 10. s?

A) 50. J
B) 12.5 J
C) zero
D) 25. J
E) 22. J

Question 42

The resultant force you exert while pressing a key on the keyboard of your new computer, for a 1.0-s period, is plotted in Figure 5-5.
Figure 5-5

How much work did you do during this 1-s interval?

A) 12.5 J
B) 50. J
C) zero
D) 22. J
E) -25. J

Question 43

A 10. kg mass, hung onto a spring, causes the spring to stretch 2.0 cm. The spring constant is

A) 49 N/cm
B) 0.20 N/cm
C) 20. N/m
D) 5.0 N/cm
E) 0.0020 N/cm

Question 44

A spring is characterized by a spring constant of 60. N/m. How much potential energy does it store, when stretched by 1.0 cm?

A) 0.3 J
B) 6.0 $\mu$ J
C) 60. J
D) 0.003 J
E) 600. J

Question 45

You lift a 10. lb physics book up in the air a distance of 1 ft, at a constant velocity of 0.5 ft/s. The work done by gravity is

A) +10 ft.lb.
B) +5 ft.lb.
C) -5 ft.lb.
D) -10 ft.lb.
E) zero.

Question 46

NOTE: The following question(s) refer(s) to the Cyclone, the famous roller coaster ride at Coney Island, shown in the sketch. Assume no friction.


-Refer to Figure 5-6. How much work was required to bring the 1000-kg roller coaster from point P to rest at point Q at the top of the 50. m peak?

A) 75. kJ
B) 50. kJ
C) 0.49 MJ
D) 32. kJ
E) 0.25 MJ

Question 47

NOTE: The following question(s) refer(s) to the Cyclone, the famous roller coaster ride at Coney Island, shown in the sketch. Assume no friction.


-Refer to Figure 5-6. If the roller coaster leaves point Q from rest, how fast is it traveling at point R?

A) 0.98 km/s
B) 22 m/s
C) 51 m/s
D) 31 m/s
E) 0.49 km/s

Question 48

NOTE: The following question(s) refer(s) to the Cyclone, the famous roller coaster ride at Coney Island, shown in the sketch. Assume no friction.


-Refer to Figure 5-6. If the roller coaster leaves point Q from rest, what is its speed at point S (at the top of the 25. m peak) compared to its speed at point R?

A) zero
B)

C) 1/

D) 2
E) 4

Question 49

NOTE: The following question(s) refer(s) to the Cyclone, the famous roller coaster ride at Coney Island, shown in the sketch. Assume no friction.


-Refer to Figure 5-6. How fast must the coaster be moving at P in order to coast to a stop at Q?

A) 9.8 m/s
B) 0.98 Km/s
C) 31 m/s
D) 0.49 Km/s
E) 22 m/s

Question 50

A toy rocket, weighing 10. N, blasts off from ground level. At the exact top of its trajectory, its energy is 140. J. To what vertical height does it rise?

A) 1.4 km
B) 1.4 m
C) 0.12 km
D) 12. m
E) 14. m

Question 51

Assuming negligible friction, what spring constant would be needed by the spring in a "B-B gun" to fire a 10. gram pellet to a height of 100 meters if the spring is initially compressed 10. cm?

A) 2.0 × 10³ N/cm
B) 200. N/m
C) 20. N/cm
D) 20. N/m
E) 2.0 × 10^-3 N/m

Question 52

If a spring-operated gun can shoot a pellet to a height of 100. m on Earth, how high could the pellet rise if fired on the moon?

A) 16.7 m
B) 100. m
C) 3600. m
D) 3.60 km
E) 600. m

Question 53

A simple pendulum, consisting of a mass m, is attached to the end of a 1 yd length of string, as shown in Figure 5-7.
Figure 5-7

If the mass is held out horizontally, and then released from rest, its speed at the bottom of the swing is about

A) 1.3 m/s.
B) 4. m/s.
C) 10. m/s.
D) 2. m/s.
E) 30. m/s.

Question 54

What is the minimum energy needed to lift 1.0 kg to a height of 200. km and to give it a speed of 8.0 km/s? (Neglect the small decrease of "g" over that distance.)

A) 34. MJ
B) 34. kJ
C) 34. J
D) 34. GJ
E) 34. TJ

Question 55

A boy releases his 2.0 kg toy, from rest, at the top of a sliding-pond inclined at 20° above the horizontal. What will the toy's speed be after sliding 4.0 m along the sliding-pond? The coefficient of kinetic friction is 0.20.

A) 3.0 m/s
B) 2.2 m/s
C) 5.2 m/s
D) 4.4 m/s
E) 3.5 m/s

Question 56

A 30. N stone is dropped from a height of 10. m, and strikes the ground with a velocity of 13. m/s. What average force of air friction acts on it as it falls?

A) 4.1 N
B) 2.9 N
C) 0.13 KN
D) 7.2 N
E) 1.2 N

Question 57

A skier, of mass 60. kg, pushes off the top of a frictionless hill with an initial speed of 4.0 m/s. How fast will she be moving after dropping 10. m in elevation?

A) 15. m/s
B) 49. m/s
C) 0.15 km/s
D) 10. m/s
E) 0.20 km/s

Question 58

A 1.0 kg flashlight falls to the floor. At the point during its fall when it is 0.70 m above the floor, its potential energy exactly equals its kinetic energy. How fast is it moving?

A) 45 m/s
B) 6.9 m/s
C) 14 m/s
D) 3.7 m/s
E) 9.8 m/s

Question 59

One horsepower is equal to

A) 746. J.
B) 550. J.
C) 550. kW-h.
D) 550. watts.
E) 746. watts.

Question 60

-The force that a squirrel exerts on a nut it has found is observed over a 10. second interval, as shown in Figure 5-8. What was the average power exerted by the squirrel?

A) 1.3 W
B) zero
C) 2.5 W
D) 5.0 W
E) 2.2 W

Question 61

My 5.0 hp mower would be equivalent to an electric mower rated at what power?

A) 0.78 KW
B) 2.8 W
C) 3.7 KW
D) 0.25 KW
E) 2.8 KW

Question 62

My battery charger uses 12. watts. At 6.0 cents per kilowatt-hour, how much does it cost to charge batteries for 24. hours?

A) 0.74 cents
B) 2.3 cents
C) 1.7 cents
D) 0.28 cents
E) 1.4 cents