Return to Honors Physics Home Page
Go to WPE Short Answer Problems
Go To Solutions (Revised 4-22-05)
WORK, POWER and ENERGY PROBLEMS
1. (A) Calculate the work required to raise 120 lb to a height of 15 ft.
(B) How much work is required to lift 250 grams a distance of 215 cm?
2. How much work (in ft-lbs) is required to carry a 50-lb sack up two flights of stairs in an apartment house if the vertical distance between each floor is 11 ft?
3. A 500 kg horse climbs to a height of 1,000 meters. What is its change in potential energy at its new location?
4. A 50 kg boy climbs to the top of a 300 meter mountain peak. What is the boy’s increase in potential energy?
5. A 1,825 lb racing car and driver is traveling at 150 mi/hr. What is the car’s kinetic energy?
6. A 3,900 lb car was driven to the top of a 5,500 ft high mountain in 20 minutes.
(A) What is the car’s increase in potential energy?
(B) How much power must be developed by the car’s engine?
7. The hopper of a concrete hoist is capable of holding 750 lb when it is half full. If this hopper is moved to an elevation of 165 ft in 6sec.
(A) What is the increase in potential energy?
(B) What power, in H.P., must be developed?
(C) What power, in watts, must be developed?
8. An elevator with 6 passengers weighs 1,400 lb. How much power must be developed if the elevator travels at 4.4 ft/sec?
9. A 6 ton tree is pulled through the forest by a tractor a distance of 500 ft. in 10 minutes. If the coefficient of sliding friction between the tree and the ground is 0.65.
(A) What force is needed to move the tree?
(B) How much work must be completed?
(C) How much power must be developed?
10. An 8,500-lb car increases its velocity from 35 mi/hr to 55 mi/hr in 6 seconds.
(A) What is its change in kinetic energy?
(B) What power had to be developed?
11. A coal elevator in a mine shaft weighs 6 tons when loaded. What minimum power must be developed to lift this car 400 ft in one minute?
12. From what height must a 100 lb boulder fall in order to have the same amount of kinetic energy as a 5 ton truck that is traveling 30 mi/hr along a level road?
13. A 56 H.P. hoist lift is able to lift objects at a steady velocity of 168 ft/min. What maximum load may be lifted with this hoist without exceeding its rated output?
14. A pump is used to move 103 m3/hr from a river into a reservoir, a total lift of 120 meters. What minimum power is needed to accomplish this task? (One m3 of water has a mass of 103 kg)
15. A 1,500 lb ball is raised 30 ft in 2 minutes. What power must be developed?
16. If the weight of the ball in problem #15 were reduced to one-half its value while the height to which it is raised is doubled with the time to accomplish the task remaining constant, what power would be required under these new conditions?
17. (A) What potential energy is possessed by a 50 kg object when it is at a height of 64 meters?
(B) If this object is then allowed to fall, what will be its velocity just as it strikes the ground?
(C) What will be its kinetic energy just as it strikes the ground?
18. A 150 kg wagon is pulled by its handle which makes an angle of 40o with the horizontal. The coefficient of rolling friction is 0.85. How much work is done in pulling the wagon a distance of 780 cm?
19. A ski lift utilizes a 78.5 kilowatt motor to keep the tow rope moving at a constant velocity. If the average person using the ski lift has a mass of 77 kg, (including the lift chair) and the lift carries the skiers to top of the mountain at an average vertical velocity of 3 m/sec, find:
(A) The maximum number of skiers allowed on the lift at one time without exceeding the rated power of the motor?
(B) The total change in energy of the skiers, if they are lifted to a height of 937m?
20. An 870 gram basketball is dropped to the floor from a height of 2.2 meters and it rebounds back to a height of 0.98 meters.
(A) What was the velocity of the ball just as it struck the floor?
(B) What was the velocity of the ball just after it left the floor?
(C) How much energy, if any, was lost during the collision with the floor?
21. You are a 98 kg laborer who was hired by the local moving company to help him move a 696.41 kg safe onto the back of a large truck whose bed is 3.1 meters above the ground. You discover that you are not strong enough to lift safe and there is no one around to help you. Therefore, you decide to devise a pulley system to assist you in completing the assigned task.
(A) Draw a diagram that illustrates the pulley system(s) that you could build that uses the minimum number of supporting strands.
(B) How much work must you put into the system?
(C) How much work will you get out of the system?
22. In your new employment on the docks of a trucking company, you are required to slide a 235 kg crate across the floor where the coefficient of sliding friction is 0.345. To accomplish this task, you attach a bar to the back of the crate (which makes an angle of 56o with the horizontal) and then proceed to push the crate a total distance of 126 meters.
(A) How much force must you exert to move this crate at a constant velocity?
(B) How much power must you be able to develop if the crate moves at a constant velocity of 2.3 m/sec.?
23. You are driving a new 3,500 lb BMW for the first time which has an 85 horsepower engine.An emergency arises which requires you to be able to go from 35 mi/hr to 60 mi/hr in 5.6 sec.
(A) Is the engine of this car able to accomplish this feat?
(B) What will be the change in energy of the car, if it is able to accomplish this feat?
24. A 2,800 nt car rolls down a 200 m high hill and immediately starts up an adjacent hill of unknown height. The car is traveling at 32 m/sec as it goes over the crest of the second hill.
(A) What was the kinetic energy of the car at the base of the first hill?
(B) How high was the second hill?
25. A horizontal force of 800 nt is required to drag a 126 kg crate across a horizontal floor, where the coefficient of sliding friction is 0.38. This force is exerted on a rope attached to the crate which makes an inclined angle of 65o with the horizontal. It takes a worker 8 sec to move this crate a horizontal distance of 22 m.
(A) What force must be applied to the rope to successfully move the crate?
(B) How much work is required to complete this task?
(C) What power must be developed to successfully complete the task?
26. Two masses, 5 grams and 10 grams are joined together by a weightless string. The string is hung over a frictionless pulley and the weights are then allowed to move freely from rest.
(A) Find the total change in potential energy after the two weights have moved 2 m in 2 sec.
(B) Find the kinetic energy of EACH weight also after 2 sec.
27. A 1.4 nt baseball is thrown vertically upward with an initial velocity of 25 m/s.
(A) To what maximum height will it rise?
(B) What will be the ball’s change in kinetic energy?
(C) What will be the ball’s change in potential energy?
(D) How much power will be developed by the ball when it returns to the ground?
28. An object is moving horizontally with a velocity of 25 m/s when it meets a smooth frictionless surface that is inclined at 25 degrees to the horizontal.
(A) How far up the incline will this object travel prior to coming to rest?
(B) What will be its change in potential energy?
(C) How much power must be developed for it to reach the point where it stops?
29. A 178 nt Will E. Coyote is on a skateboard. He has a velocity of 12 m/s as he comes over the crest of one hill. A short time later, he discovers that he has a velocity of 36 m/s and that he is at the base of the hill.
(A) What is the height of this hill?
(B) What is his change in potential energy?
30. A 34 kg wagon is pulled 34 m at a constant velocity of 26 m/s across a surface whose coefficient of sliding friction is 0.682. It pulled by a handle that is attached to the front of the wagon and is inclined at 55 degrees with the horizontal.
(A) What force must be exerted on the handle to move this wagon at a constant horizontal velocity?
(B) How much work is required to complete the assigned task?
(C) How much power must be available to complete the assigned task?
31. You are assigned to move a 4,578 nt machine by means of a pulley system onto the back of a truck whose bed is 42 cm above the ground. This task must be completed in 5.7 minutes. The cable your employer gives you has a tensile strength rating of 52 kg.
(A) What is the minimum number of strands needed for this pulley system to successfully accomplish your assigned task?
(B) Draw a diagram of one of the potential pulley systems that you could utilize.
(C) How much power must you develop in completing the assigned task?
(D) How much rope must pass through your hands in accomplishing the task?
(E) What force must you exert while lifting this piece of machinery?
32. You are driving your new dream sports car. The 746 nt car has a 63,410 watt motor and your are currently traveling at 53 m/s. You want to accelerate to 89 m/s in 2.6 sec.
(A) Are you able to accomplish this movement?
(1) If you are, what is the change in energy of the car?
(2) if not, how fast will you be traveling after 2.6 sec.?
(B) How much time would it take you to
accelerate from 53 m/s to 89 m/s with the rated power of your motor?
33. A 67 kg crate is being pulled up a 34 m long inclined plane which makes an angle of 82 degrees with the horizontal.
(A) What is the coefficient of sliding friction of this surface, assuming that IF you stopped pulling on the box and gave it a light tap, it would begin to slide down the inclined plane with slow but steady motion.
(B) How much work must you do in moving this crate up the inclined surface?
(C) How much power must you develop if you are required to complete the assigned task in 2.1 minutes?
(D) How much work would be performed in simply lifting the crate vertically?
(E) Compare the work performed using the ramp and simply lifting the load. Why is there such a difference in magnitude? You must mention in you discussion the effect of angle of inclination and coefficient of friction.
34. You are a manager at a local grocery store and are processing a new shipment of meats. Using a pulley combination requiring only 334 Nt of your effort, you must lift a 210.6 kg crate of fresh "Coyne's Country Clucker" chicken breasts onto a table 0.81 m high.
(A) Calculate the minimum number of strands needed to support the crate.
(B) How many meters of rope must you pull through this system?
(C) Diagram the pulley combination used to accomplish this task.
(D) What is the real mechanical advantage of this system, and what is the meaning of this value?
(E) What is the efficiency of this system?
(F) Why is there a difference between the work in and work out associated with the use of this pulley system?
35. A box is being pulled, by a winch that is rated at 95 watts, at a constant velocity of 2.38 m/s up a board onto a truck. The board is used as an inclined plane and is situated such that the top surface of the board makes an angle of 22o, with the end of the board that touches the ground located 5 meters from the back of the truck. What is the maximum mass allowable for this box so as not to exceed the rated power of the winch?
36. A 65 kg crate is being pulled up an inclined surface that makes an angle of 22o with the horizontal. In order to pull this crate up this surface, a cable is attached to the front of the crate such that it makes an angle of 15o with the surface of the inclined plane.
(A) What force must you exert against the cable to move this crate up the inclined surface at a constant velocity of 2.78 m/s?
(B) How much power will you have to develop to accomplish this task?
37. Suppose we have a fifty (50 ft) foot deep well from which we draw 200 ft3 of water per minute. (1 ft3 of water weighs 62.4 lb) Please find the following:
(A) The potential energy of the water at the top of the well.
(B) The amount of work needed to raise the water to the top of the well.
(C) The horsepower that needs to be
developed.
38. A 3,200 lb car is at the top of a 100 ft high cliff. Find the following requested information:
(A) The potential energy of the car at the top of the cliff.
(B) The velocity at which the car would strike at the base of the cliff if it were to go over the edge.
(C) The kinetic energy of the car at the base, just as it strikes.
(D) The power developed due to the car striking the ground at the bottom of the cliff.
39. A 100 lb box is located on the floor. You exert 40 lb to push the box a distance of ten (10) ft in 25 seconds. You then lift the box onto a 2.5 ft high lab table in 2 seconds.
(A) How much work did you do in each phase of moving the box?
(B) How much power (in watts, and H.P.) during each phase of moving the box?
40. Compute the horse power that must be developed to raise 6 tons of coal to a height of 60 ft in 5 minutes.
41. In an experiment to determine the coefficient of friction, a 14 kg wooden block is pulled at a constant speed along a table top by means of a spring whose constant of elasticity is known to be 60 nt/m. If the spring’s length increases from 7.5 cm to 16.5 cm while the box is being pulled, what is the coefficient of sliding friction between the box and the table top.
42. A basketball with a mass of 675 g is dropped to the floor from a height of 2.45 m and it rebounds back to a height of 1.85 m.
(A) What is the velocity of the ball just as it strikes the floor?
(B) What is the velocity of the ball just as it leaves the floor?
(C) How much energy, if any, is lost during the ball's collision with the floor?
43. Calculate the minimum number of strands needed to support a 305 kg object using a 425 Nt sandbag. If the object is to be lifted onto a cart that is 1.6 m above the floor, how much rope must you pull through this system? Diagram a pulley combination that will enable you to accomplish this task.
44. A ski lift employs a 55 kilowatt, 55% efficient, motor to move skiers through a vertical lift of 1500 meters. Each skier, including the chair, has a weight of 800 Nt, and must be moved at a uniform velocity of 6 m/sec up the slope. If the slope makes an angle of 55° with the horizontal, what is the maximum number of skiers allowed on the lift without exceeding the output of the motor?
45. Joe Schmutz does not believe in using
pulleys (his grandfather received the nickname "Slim" by fellow
workers in 1934, after being pulled through a twelve-pulley system when he
failed to let go of the rope). So, Joe builds a
(A) Neglecting the effect of friction, what FORCE must Joe exert on the box to move it up the plank?
(B) How much WORK does Joe perform using the RAMP?
(C) What POWER must he develop to accomplish his task?
(D) How much WORK would Joe perform if he decided to LIFT the box vertically onto the table?
(E) If the coefficient of sliding friction associated with the ramp is 0.238, what additional power must Joe supply to move the crate?
46. A golf ball with a mass of 225 grams strikes a tree limb directly above where Jennifer is standing. It drops a distance of 10.5 m onto her head, then rebounds back to a height of 1.35 m above her head.
(A) What is the velocity of the ball just as it strikes Jennifer?
(B) What is the velocity of the ball just as it leaves her head?
(C) How much energy, if any, is lost during the ball's collision with her head? Determine this value by using both difference in potential energy and difference in kinetic energy methods.
47. As a young engineer, you have been hired by Gerrity's Supermarket to design an access ramp leading to the entrance of the store. The ramp is expected to allow a shopper to push a cart up the ramp with a force of 50 Nt, which has been shown to be an acceptable exertion. Will a slope of 5° be too steep, assuming the mass of an average grocery cart loaded with groceries is 30 kg? Assume friction between the wheels on the axles results in a coefficient μ K = 0.10.
48. A 500 kg box is pulled up an incline 200 m in height at a constant velocity in 1.00 minutes. The incline is 300 m in length.
(A) Write a mathematical expression for FE.
(B) What assumptions can you make or are not permitted to make about the following:
(1) the relationship between FE, FP, and FK.
(2) μ K.
(C) How much work is required to accomplish this task, now assuming μ K = 0.21.
(D) How much power must be developed?
(E) Can you use the information provided to solve for μ K?
49. The conveyor at your factory utilizes a 400 hp, 90% efficient, motor to move 250-lb air conditioner units to the 3d floor of a warehouse 18 feet above ground level. The units move on the conveyor with a speed of 12 ft/sec, and the conveyor is elevated 45° relative to the horizontal. What is the maximum number of units allowed on the conveyor at one time, without exceeding the output of the motor?
50. A truck, traveling at 5 m/sec, runs out of gas as it passes the crest of a 20 meter incline. The truck proceeds to roll down this incline and starts up the next. The truck and its occupants weigh 1000 Nt.
(A) How fast is the truck moving when it reaches the bottom of the first incline?
(B) At what elevation up the next incline must the truck be towed to take it to the top of the next hill of unknown height?
Multiple Choice
1. Work is measured in the same units as:
(A) momentum (C) power
(B) energy (D) force
2. A ball is thrown vertically upward into the air. As it rises, there is an increase in:
(A) kinetic energy (C) potential energy
(B) momentum (D) power
3. As the velocity of a body is halved, its kinetic energy is:
(A) halved (C) doubled
(B) reduced to one-fourth (D) quadrupled
4. Work is done when:
(A) an effort is exerted (C) a push is applied
(B) a table supports a book (D) a force causes motion
5. The expression (Force)(Distance)/(time) is used to determine:
(A) work (C) power
(B) energy (D) resistance
6. In order to compute power, one must know:
(A) force and time (C) work and distance
(B) distance and time (D) energy and distance
(E) force, distance, and time
7. If the weight of a pile driver is doubled, its potential energy is doubled.
(A) True (B) False
8. Power depends on all of the following factors EXCEPT:
(A) force (C) distance
(B) elasticity (D) time
9. Energy is recorded in the same units as:
(A) work (C) momentum
(B) power (D) inertia
10. The potential energy of an object varies directly as its:
(A) height and weight (C) speed and mass
(B) speed and height (D) height and specific gravity.
11. In a waterfall, energy is converted from:
(A) kinetic to potential (C) potential to kinetic
(B) electrical to kinetic (D) speed and distance
12. The kinetic energy of an object depends upon its:
(A) elasticity (C) mass and resiliency
(B) speed and mass (D) speed and distance
13. The energy of motion is:
(A) chemical (C) potential
(B) static (D) kinetic
14. Which of the following does not possess pure potential energy?
(A) falling water (C) a bent spring
(B) compressed air (D) a stone lying on the brink of a steep mountain wall
15. One watt is the same as:
(A) energy (C) work
(B) power (D) force
16. Potential energy is defined as the ability of an object to do work because of;
(A) gravity (C) velocity
(B) mass (D) elevation
17. The potential energy of an object varies:
(A) directly as the square of its mass. (B) inversely as the square of its mass.
(C) inversely as its mass. (D) directly as its mass.
18. Upon which factor does potential energy NOT depend?
(A) time (C) force
(B) gravity (D) distance
19. A body has a mass “m” and moves with a velocity “v”. If its mass is tripled, its velocity remains constant, the kinetic energy is:
(A) the same (C) 3 times greater
(B) 18 times greater (D) 6 times greater
20. The decrease in potential energy of a 5 lb weight when it falls 15 ft is:
(A) 3 ft-lb (C) 15 ft-lb
(B) 5 ft-lb (D) 75 ft-lb
21. The potential energy of 100 grams of copper raised to a height of 500 cm with respect to that of 100 grams of aluminum raised to the same height:
(A) less than (C) equal to (B) greater than
22. A boy walks up a flight of stairs in 1 minute. If he had walked up the same flight in 2 minutes, the work done would have been:
(A) half as much (C) twice as much
(B) the same (D) quadrupled
(E) reduced to one-fourth
23. The watt is a(n):
(A) erg/sec (C) joule-sec
(B) joule/sec (D) slug/sec
24. The unit of work in the MKS system is the:
(A) erg (C) joule
(B) dyne (D) foot-lb