AP Physics 1 Assignment – Energy, Work, and Power

Reading   Chapter 7, Open Stax College Physics; Chapter 6, Giancoli

 

 

Objectives/HW

 

 

The student will be able to:

HW:

1

Define and apply the concepts of kinetic and potential energy and use the conservation of energy to explain physical phenomena.

1 – 5

2

Calculate mechanical kinetic energy and gravitational potential energy (in joules) and use conservation of energy to solve related problems.

6 – 16

3

Define and calculate work and solve related problems.

17 – 23

4

Relate and equate work and energy and solve related problems.

24 – 30

5

Solve problems involving work and energy for a mass attached to a spring.

31 – 34

6

Define and calculate power (in watts or horsepower) and solve related problems.

35 – 42

7

Solve problems involving machines and efficiency.

43 – 46

 

 

Homework Problems

 

1.     Old-fashioned alarm clocks have springs that you Òwind upÓ.  What type of energy does the spring have after it is wound?  As the alarm clock runs and performs its various functions the spring loses this energy – what becomes of it?  In other words, the energy initially in the spring is changed into what other forms?

2.     Describe the energy transformations that occur when an athlete is pole vaulting.  Trace the changes in energy starting with the athlete standing at rest, then running, then going up and over the bar, and ending at rest on the big ÒcushionÓ that they land on. 

3.     In mountainous areas, road designers build escape ramps to help stop trucks with failed brakes.  These escape ramps are usually roads made of loose gravel that go up hill.  Describe changes in forms of energy when a fast-moving truck uses one of these escape ramps.

4.     As you have already learned, the value of many physics concepts depends upon and is relative to a frame of reference.  Are values of energy relative to a frame of reference?  Would the change in an objectÕs energy be relative to a frame of reference?  Explain.

5.     A lump of clay is thrown against the wall and sticks there.  Right before it hits the lump has both potential energy and kinetic energy.  After it hits it still has the same potential energy but it stops moving.  Has energy been conserved?  If so what happened to the kinetic energy?  Explain.

6.     Mr. M drives his 1300 kg car at speeds around 25 m/s (56 mph).  (a) How much kinetic energy does this represent?  (b) Suppose he is passed by a truck with twice the mass and going 40% faster – 35 m/s (78 mph).  How much more kinetic energy does the truck have?

7.     Throughout time Earth has been pummeled by impacts from space debris – asteroids, meteoroids, comets, etc.  An object the size of Farragut High School might hit the Earth about once every few thousand years.  Such an object might have a mass of 1.5 × 109 kg and a speed of around 60 km/s.  Scientists estimate the explosive energy of such an impact by calculating the objectÕs kinetic energy.  Do this.  Convert your answer to Megatons of TNT equivalent (a unit for measuring nuclear bombs – a Megaton of TNT releases 4.2 × 1015 J).

8.     Two floors in a building are separated by 4.1 m.  People move between the two floors on a set of stairs.  (a) Determine the change in potential energy of a 3.0 kg backpack carried up the stairs.  (b) Determine the change in potential energy of a person with weight 650 N that descends the stairs.

9.     A physics student decides to Òburn offÓ some Calories by climbing a ladder.  As the ladder is ascended, some food energy is being converted to gravitational potential energy.  (a) If the student has a mass of 75 kg, how tall a ladder is needed to burn off one Calorie (4190 J)?  (b) Conversely, if the student only has a 3.5 m ladder, how much additional mass must he carry up with him to burn off the Calorie?

10.  A 20.0 kg rock falls from the edge of a 100 m cliff.  (a) Determine the energy of the rock relative to the bottom of the cliff.  (b) Determine the impact speed. 

11.  A 100.0 gram ball is thrown straight down from a height of 2.0 m.  The ball strikes the floor at a speed of 7.5 m/s.  (a) How much kinetic energy does it gain?  (b) With what speed was the ball thrown downward? 

12.  (a) A pendulum has maximum speed v as it swings back and forth.  Use energy conservation to derive an expression for its greatest height h above its low point in terms of v and appropriate constants.  (b) A different pendulum with period T swings back and forth with the string reaching a maximum angle θ relative to vertical.  Derive an expression for its maximum speed v in terms of T, θ, and appropriate constants assuming it undergoes simple harmonic motion.

13.  A skateboarder with mass 76.5 kg skates back and forth in a "half pipe" (a semicircle) with radius 8.00 m.  Use the lowest point in the pipe as a reference for PE.  Ignore friction.  (a) In order to get vertical (i.e. reach the lip of the half pipe), what speed must the skater have at the lowest point in the pipe?  (b) What is the total energy of the skater?  When the skater reaches a point 2.00 m higher than the lowest point find:  (c) the skater's potential energy, (d) the skater's kinetic energy, and (e) the skater's speed.

14.  Starting at rest, Tarzan swings on the end of a vine, lets go, flies through the air, and lands atop a branch of a tree.  The vine is 30.0 m long and initially forms an angle of 45.0¼ with the vertical.  The branch is 25.0 m lower in elevation than the pivot point of the vine.  (a) Find TarzanÕs maximum speed.  (b) Find his speed as he lands on the branch.

15.  A kid throws a 4.90 N rock off a bridge that is 25.0 m above the water.   The initial velocity is 13.0 m/s, 0¡.  (a) Find the total energy of the rock.  (b) Find the rock's speed as it hits the water.  (c) Which results would be different if the rock was thrown in a different direction?  Explain.

16.  An arrow of mass 25.0 g is observed to strike the ground with velocity 30.0 m/s, 330.0¼.  Assuming it was launched from somewhere by a hunterÕs bow, what was the maximum height and potential energy attained by this arrow in its flight, relative to its point of impact?  Ignore air resistance.  Hint:  recall the properties of projectile motion!

17.  Describe any and all situations or circumstances in which a force acting on an object does: (a) zero work, (b) positive work, and (c) negative work. 

18.  A boy pushes horizontally with 80 N of force on a 20 kg box 10 m across a floor.  The coefficient of friction is 0.40.  (a) Find the work done on the box by the boy.  (b) Find the work done on the box by friction.

19.  A weightlifter eats a candy bar that has 837 kJ (200 Calories) of energy.  In order to Òburn offÓ this candy bar he must do physical work 10.0% that amount.  How many times would he need to bench press 50.0 kg a distance of 0.50 m in order to burn off the candy bar?

20.  A sled is pulled across level snow with a force of 225 N along a rope that is 35.0¡ above horizontal.  If the sled is moved a distance of 65.3 m, how much work is done? 

21.  The escalator at Woodley Park Station is 65 m long and inclined 30¡.  Determine the work done by the escalatorÕs step acting on a 57.0 kg person that rides this distance. 

22.  A librarian picks up a 22 N book from the floor to a height of 1.25 m.  He then carries the book 8.0 m to the stacks and places the book on a shelf that is 0.35 m above the floor.  Determine how much total work he does on the book from beginning to end.

23.  A 100 kg piano is pushed at a constant speed up a 4.00 m ramp of incline 10.0¡.  It takes 220 N of force to push the piano along the ramp.  Because the piano does not accelerate the total work done on it must be zero.  (a) Find the work done by the person pushing.  (b) Find the work done by gravity.  (c) Find the work done by normal force.  (d) Find the work done by friction.  (e) Find the amount of friction. 

24.  A ball is dropped from the top of a tall building and reaches terminal velocity as it falls.  Will the potential energy of the ball upon release equal the kinetic energy it has when striking the ground?  Explain. 

25.  In the 1950Õs an experimental train that had a mass of 25,000 kg was powered across a level 500 m track by a jet engine that produced a thrust of 500 kN.  (a) Determine the work done on the train by the engine.  (b) Determine the final speed of the train, ignoring friction.

26.  A 2000 kg car with speed 12.0 m/s hits a tree.  The tree does not move or break and the front of the car is smashed inward 50.0 cm.  Ignore friction.  (a) Determine the work done on the car by the tree.  (b) Determine the amount of force involved.   

27.  A 2200 kg truck encounters an average friction force of 785 N at interstate speeds.  Suppose the truck accelerates from 25 m/s to 35 m/s over a distance of 350 m.  Determine the amount of force generated by the truckÕs drive-train in order to produce this result.

28.  A 222 kg iceboat glides with initially velocity 3.33 m/s northward across a frozen lake where m= 0.10.  The wind then exerts on the boat a constant force of 444 N, 67.5¡ (i.e. NNE) as the boat travels 111 m, 90.0¡ (i.e. due north).  Find the final speed of the iceboat.

29.  A constant upward force of 442 N is applied to a stone that weighs 32 N.  The upward force is applied through a distance of 2.0 m, and the stone is then released.  To what height, from the point of release, will the stone rise? 

30.  A girl with mass 29 kg climbs a ladder to the top of a slide, 3.8 m high.  She slides 8.0 m along the slide and attains a speed of 4.2 m/s at the bottom.  (a) Determine the work done by friction.  (b) Find the average amount of frictional force on the slide.

31.  A 1.20 kg mass on a horizontal surface is attached to a horizontal spring with constant k = 7.00 N/m and set into motion so that it oscillates back and forth on a frictionless horizontal surface.  The mass moves 10.0 cm on either side of its equilibrium position.  (a) Find its maximum rate of acceleration.  (b) Find its maximum speed.  (c) Find the time for the energy of the system to undergo a complete transformation from kinetic to potential (or vice versa). 

32.  A spring with constant k = 100.0 N/m is mounted vertically and then compressed 20.0 cm.  A 500.0 gram ball is placed on top of the spring and then the ball and spring are released.  
(a) How high above its starting position will the ball be propelled into the air?  (b) What is the ballÕs speed at the instant the spring returns to its original length?  (c) Find the maximum kinetic energy attained by the ball.

33.  A proposal is made to use a giant spring in the bottom of an elevator shaft as a means of safely ÒcatchingÓ a falling elevator car.  The car freefalls until it hits the spring, which is then compressed until the car stops.  The carÕs loaded weight is 20.0 kN.  The elevator will service 20 floors.  Distance between floors is 4.00 m.  The deceleration rate of the car should not exceed 10 gÕs as it is being stopped.  (a) Determine the requirements for the spring constant and the amount the spring will compress in order to catch the falling car in the worst-case scenario.  (b) What do you think about this proposal?  Is it practical?

34.  An object of mass m hangs from a spring and oscillates with period T.  It moves a distance d in the amount of time T.  Derive expressions for the following in terms of m, d, T, and appropriate constants:  (a) the objectÕs maximum kinetic energy, and (b) itÕs maximum speed.

35.  Two people of equal mass, Frank and Ernie, climb the same flight of stairs.  Frank does it in 25 seconds and Ernie does it in 35 seconds.  (a) Compare the amount of work – who did more or was it equal?  Explain.  (b) Compare the amount of power – who was more powerful?  Or are they equal?  Explain. 

36.  Brutus, a champion weightlifter, raises 240 kg a distance of 2.35 m.  (a) How much work is done lifting the weights?  (b) How much work is done holding the weights at rest above his head?  (c) How much work is done lowering them back to the ground?  (d) Does Brutus do any work if the weights are just dropped instead of lowered back to the ground?  (e) If the lift is completed in 2.5 s, what is the power of Brutus? 

37.  The drive-train of a 1600 kg car produces a forward force of 5300 N as it accelerates from 0 to 60.0 mph in 10.0 seconds.  (a) If this acceleration covers a distance of 125 m, determine the power output of the carÕs engine.  (b) Find the average frictional force opposing the forward motion of the car.

38.  A 3.2 kW (4.3 hp) pump delivers 550 L of oil into a barrel on a platform 25.0 m above the pumpÕs intake pipe.  The density of the oil is 0.820 g/cm3.  (a) Calculate the work done by the pump.  (b) Determine the time for the task to be completed.

39.  (a) Starting from rest an object of mass m falls freely for time t.  Determine the maximum power of gravity during the fall in terms of m, t, and relevant constants.  (b) Repeat the problem but this time the mass m slides down a frictionless ramp with inclination θ for time t.  (c) Using either result, determine a situation in which the power of gravity acting on a car of mass 1500 kg is equivalent to 100 hp.

40.  An engine moves a boat through the water at a constant speed of 15 m/s.  The engine must develop a thrust of 6.0 kN to balance the force of drag from the water acting on the hull.  Determine the power output of the engine. 

41.  A 188 W motor will lift a load at the rate of 6.50 cm/s.  How great a load can this motor lift at this speed? 

42.  A horse walking along the bank tows a barge through a canal.  The barge moves due west at 180¡ through the canal but the towrope is directed at 200.0¡.  Tension in the rope is 400 N.  (a) How much work is done in pulling the barge 1.00 km.  (b) If this is a one horsepower horse, how much time is required for the trip?

43.  An elevatorÕs electric hoist is rated at 8.0 kW and has an efficiency of 90.0%.  The hoist lifts the elevator car, mass 1225 kg, a distance of 9.00 m.  (a) How much time is required?  (b) How much electrical energy is used to perform this task?

44.  A metal ramp 6.00 m long is tilted 10.0¡ and is used to load and unload a moving van.  Suppose a 20.0 kg box is pushed up the ramp and it slides with a friction coefficient of 0.30.  The ramp can be viewed as a ÒmachineÓ where the useful output is the potential energy gain of the box and the input is the physical work done by the person doing the pushing. 
(a) Determine the efficiency of the ramp.  (b) Determine the ratio of the force needed to lift the box without the ramp to the force needed to push it along the ramp (this is called the mechanical advantage).

45.  Suppose a person uses a mechanical jack to lift one half the weight of a car with a mass of 1200 kg.  During each stroke of the jack handle, the personÕs hand is pushing for a distance of 40.0 cm but the car is lifted only 5.0 mm.  (a) Assuming the jack is 100% efficient, how much force must the person exert on the handle as the car is lifted?  (b) If the actual amount of force required on the handle is 90.0 N, what is the actual efficiency of the jack?

46.  A power output of 18.0 h.p. is required to overcome friction and move a certain car at a constant speed of 55.0 mph.  The car runs on gasoline that has an energy content of 110 MJ per gallon.  The efficiency of the engine/transmission is 15%.  (a) What is the force of friction on the car?  (b) What power input is required at 55.0 mph?  (c) How much energy is wasted every minute at 55.0 mph?  (d) Determine the fuel economy in miles per gallon.

Selected Answers

37.0%

82%

2.13

3.9 times more

342

0.650 s

15 s

35 s

8.40 minutes

47 kg

0.408 m
5.7 m

11.5 m

16.9 m

26 m

89 m

19 mpg

0.242 m/s

2.02 m/s
4.1 m/s

8.61 m/s

10.8 m/s

12.5 m/s

13.1 m/s

14.3 m/s

25.7 m/s

42 m/s

44.3 m/s

140 m/s

0.583 m/s2

49.8 N

74 N

100 N

546 N

700 N
2700 N

2.89 kN (or 295 kg)

288 kN

13.0 kN/m;

–144 kJ

–5500 J

–2700 J

–820 J

–780 J

–681 J

–199 J

0 J

1.14 J

2.0 J

2.81 J

7.7 J

120 J

165 J

800 J

880 J

1500 J

4500 J

5500 J

6000 J

12.0 kJ

18 kJ

19.6 kJ

110 kJ

120 kJ

376 kJ

410 kJ

4.56 MJ

250 MJ

640 Megatons (2.7 « 1018 J)

2200 W

66 kW (89 hp)

89.5 kW

90 kW