Work & Energy Problems

 

Physics requires  practice to develop your solving problems skills and your logical thinking . I strongly recommend to study carefully the examples, and solve the following problems in your book.

 

Examples: 6.1- 6.12  Pages. 138 - 155

Problems:  1,3,5,17,19,25,27,29,31,33,37,39,41,43,45  Pages. 162 - 164

 

 

Problems

 

1. (19E)  Two students push a dune buggy 35.0 m across a lot. The force required is 825 N. How much work is done?

 

2. (20E)   After a rain, the force necessary to push the dune buggy in Problem 19 through the mud is doubled. How does the amount of done by the students change?

 

3. (7E)   How much work is required for a mechanical hoist to lift a 9000 N automobile to a height of 1.80 m for repair?

 

 4. (12E)  How much work is done lifting a 200 – kg wrecking ball 6.50 m  above the ground ?

 

5. (14E)  The handle of vegetable wagon makes an angle of 25.0º with the horizontal (fig). If the peddler exerts a force of 35.0 lb  along the handle, how much work does the peddler do in pulling the cart 1.00 mi ? 

 

6. (16E)  A man pulls a sled a distance of 231 m. The rope attached to sled makes an angle of 30.0º with the ground. The man exerts a force of 775 N on the rope. How much work does the man do in pulling the sled?

 

7. (5E)   The work required to lift a crate  is 310 J. If the crate  is lifted in 25.0 s, what power is developed?

 

8. (9E)  How long would it take a 950-W motor to raise a 360-kg mass to a height of 16.0m?

 

9. (14E)  How long would it take a 4.50-kW motor to raise a 175-kg boiler to a platform 15.0 m above the floor? 

 

10. (19E)  A motor on an escalator is capable of developing 12 kW of power.

a)      How many passengers of mass 75 kg each can it lift a vertical distance of 9.0 m per min, assuming no power loss?

b)      What power, in kW, motor is needed to move same number of passengers at the same rate if 45 %  of the actual power developed by the motor is lost to friction and heat loss?

 

11. (21E)  A pallet weighing 575 N is lifted a distance of 20.0 m vertically in 10.0 s. What power is developed in kilowatts?

 

12. (22E)  An ironworker carries a 7.50-kg tool bag up a vertical ladder on a high-rise building under construction.a) After 30.0 s, he is 8.20 m above his starting point. How much work does the worker do on the tool bag ?b) What is the average power developed by the worker?     

 

13. 6E)  A bullet with mass 12.0g  travels 415 m/s. Find its kinetic energy. ( Hint: Convert 12.0 g to kg )

 

14. (8E)  A crater of mass 475 kg is raised to a height 17.0 m above the floor. What potential energy has it acquired with respect to the floor?

 

15. (10E)  The potential energy of a girder , after being lifter to the top of a building, is 5.17 x 105  ft lb. If its mass is 173 slugs, how high is the girder?

 

16. (13E)  A 250-kg part falls from a plane and hits the ground at 150km/h. Find its kinetic energy.

 

17. (14E) A meteorite is a solid composed of stone and/or metal material from outer space that passes through the atmosphere and hits the earth’s surface. Find the kinetic  energy of a meteorite with mass 250 kg that hits the earth at 25 km/s.

 

18. (13V)  A weight lifter raises a 100-kg barbell to a height of 2.0 m.. What is the barbell’s potential energy?

 

19. (15V)   A windsurfer and sailboard have a combined mass of 90 kg. What is their kinetic  energy when they are going 10 m/s ?

 

20. (17V)   The kinetic energy of a motorcycle and rider is 60,000 J. If  their total  mass is 300 kg, what is their speed?  

 

21. (19V)   A worker at top of a 629-m-tall television transmitting tower in North Dakota accidentally drops a heavy tool. If air resistance  is negligible, how fast is the tool going just before it hits the ground?

 

22. (21V)   A child on a swing has a speed of 7.7 m/s at the low point of the are ( · Figure 3.46). How high will the swing be at the high point?

 

23. (23V)   In the Drop Tower at Bremen, Germany, the 300-kg test chamber falls freely from a height of 110 m.

a)      What is the chamber’s potential energy at the top of the tower?

b)      How fast is it going when it reaches the bottom of the tower?

(  You may  want to convert you answer to  mph  for comparison to highway speeds)

 

24. (25V)   A bicycle and rider going 10 m/s approach a hill. Their total mass is 80 kg.

a)      What is their kinetic energy?

b)      If the rider coasts up the hill without pedaling, at what point will the bicycle come to a stop?

 

25. (27V)   The ceiling of an arena is 20 m above the floor. What is the minimum speed that a thrown ball would have to reach the ceiling?

 

26. (29V)   Compute how much kinetic energy was “lost” in the collision in Problem  7

 

27. (31V)   How long does it take a worker producing 200 W of power to do 10,000 J of work?

 

28. (33V)   A professor’s little  car can climb a hill in 10 s. The top  of the hill is 30 m higher than the bottom, and the car’s mass is 1,000 kg. What is the power output of the car? 

 

29. (35V)   A bicyclist rides to the top of Mt. Nebo Arkansas, in 23 min. The vertical height that the bicyclist climbs is 360 m, and the total mass of bicycle and rider is 85 kg. What was the bicyclist’s power output?

 

30. (16E) Oil is pumped at 25.0 m3/min  into a tank 10.0m above the ground.( 1 L of oil has a mass of 0.68 kg. )

a)  What power, in kW, must be delivered by the pump?

b)  What is the increase in potential energy of the after 10.0 min?

c)   Find the increase in potential energy of the oil after 10.0 min if the tank is 5.00 m above the ground

 

31.(3G)  A 1300-N crate rests on the floor. How much work is required to move it at constant speed (a) 4.0 m along the floor against a friction force of 230 N, and (b) 4.0 m vertically?

32.(5G)    (II) A box of mass 5.0 kg is accelerated by a force across a floor at a rate of  m/s2 for 7.0 s. Find the net work done on the box.

 

33. (1 S).A block of mass 2.50 kg is pushed  2.20 m along a frictionless horizontal table by a constant 16.0-N force directed 25.0° below the horizontal.  Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, and (c) the gravitational force.   (d) Determine the total work done on the block.

 

34. (7S) A force F = ( 6 i - 2 j ) N acts on a particle that undergoes a displacement Δr = ( 3 i + j) m.  Find (a) the work done  by the force on the particle and (b) the angle between F and Δr.

 

35. (12G) The force on an object, acting along the x axis, varies as shown in Fig. 6–37. Determine the work done by this force to move the object (a) from  to  and (b) from  to

 

36. (11S) The force acting on a particle varies as in Figure P7.11. Find the work done by the force on the particle as it moves (a) from  x = 0 to x = 8.00 m, (b) from x = 8.00 m to  x = 10.0 m, and (c) from x = 0 to x = 10.0 m.

 

37.(12S)   The force acting on a particle is  Fx = (8x – 16) N, where x is in meters. (a) Make a plot of this force versus x from x = 0 to x = 3.00 m.  (b) From your graph, find the net work done by this force on the particle as it moves from x = 0 to x = 3.00 m.

 

38.(14S) A force F = ( 4x i + 3y j ) N acts on an object as the object moves in the x direction from the origin to x = 5.00 m.  Find the work W = òF×d done on the object by the force.

 

39.(17G) How much work is required to stop an electron m = 9.11 x 10 31 kg) which is moving with a speed of 1.90 x 10 6 m?

 

40.(19G) An 88-g arrow is fired from a bow whose string exerts an average force of 110 N on the arrow over a distance of 78 cm. What is the speed of the arrow as it leaves the bow?

41.(20G) A baseball  traveling  moves a fielder’s glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?

42.(25G) A 285-kg load is lifted 22.0 m vertically with an acceleration  by a single cable. Determine (a) the tension in the cable, (b) the net work done on the load, (c) the work done by the cable on the load, (d) the work done by gravity on the load, and (e) the final speed of the load assuming it started from rest.

43.(26S) A 3.00-kg object has a velocity ( 6.00i - 2.00j )m/s.  (a) What is its kinetic energy at this time? (b) Find the total work done on the object if its velocity changes to ( 8.00i + 4.00j ).  (Note: From the definition of the dot product,

v2 = v·v.)

 

 Situations Involving Kinetic Friction

 

44. (31S) A 40.0-kg box initially at rest is pushed 5.00 m along a rough, horizontal floor with a constant applied horizontal force of 130 N.  If the coefficient of friction between box and floor is 0.300, find (a) the work done by the applied force, (b) the increase in internal energy in the box-floor system due to friction, (c) the work done by the normal force, (d) the work done by the gravitational force, (e) the change in kinetic energy of the box, and (f) the final speed of the box.

 

45.(32S)A 2.00-kg block is attached to a spring of force constant 500 N/m .  The block is pulled 5.00 cm to the right of equilibrium and released from rest.  Find the speed of the block as it passes through equilibrium if (a) the horizontal surface is frictionless and (b) the coefficient of friction between block and surface is 0.350.

 

46.(36S) The electric motor of a model train accelerates the train from rest to 0.620 m/s in 21.0 ms. The total mass of the train is 875 g.  Find the average power delivered to the train during the acceleration.

 

Potential Energy

 

47(29G) A 1200-kg car rolling on a horizontal surface has speed  when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?

 

48(33G) Jane, looking for Tarzan, is running at top speed  and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward? Does the length of the vine affect your answer?

 

49.(35G) A sled is initially given a shove up a frictionless 28.0º incline. It reaches a maximum vertical height 1.35 m higher than where it started. What was its initial speed?

 

50.(39G) A vertical spring (ignore its mass), whose spring stiffness constant is  is attached to a table and is compressed down 0.150 m. (a) What upward speed can it give to a 0.30-kg ball when released? (b) How high above its original position (spring compressed) will the ball fly?

 

51.(43G) The roller-coaster car shown in Fig. 6–41 is dragged up to point 1 where it is released from rest. Assuming no friction, calculate the speed at points 2, 3, and 4.

 

52.(52G) A 110-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 350 N. For the first 15 m the floor is frictionless, and for the next 15 m the coefficient of friction is 0.30. What is the final speed of the crate?

 

53.(37G) A 65-kg trampoline artist jumps vertically upward from the top of a platform with a speed of  (a) How fast is he going as he lands on the trampoline, 3.0 m below (Fig. 6–38)? (b) If the trampoline behaves like a spring with spring stiffness constant  6.2 x 104 how far does he depress it?

54.(39G) A vertical spring (ignore its mass), whose spring stiffness constant is  is attached to a table and is compressed down 0.150 m. (a) What upward speed can it give to a 0.30-kg ball when released? (b) How high above its original position (spring compressed) will the ball fly?

 

55.(7S)   A glider of mass 0.150 kg moves on a horizontal frictionless air track.  It is permanently attached to one end of a massless horizontal spring, which has a force constant of 10.0 N/m both for extension and for compression.  The other end of the spring is fixed.  The glider is moved to compress the spring by 0.180 m and then released from rest. Calculate the speed of the glider (a) at the point where it has moved 0.180 m from its starting point,

 

56.(11S) A block of mass 0.250 kg is placed on top of a light vertical spring of force constant 5 000 N/m  and pushed downward, so that the spring is compressed by 0.100 m. After the block is released from rest it travels upward and then leaves the spring.  To what maximum height above the point of release does it rise?

 

57.(13S)Two objects are connected by a light string passing over a light frictionless pulley . The object of mass 5.00-kg is released from rest. Using the principle of conservation of energy, (a) determine the speed of the 3.00-kg object just as the 5.00-kg object hits the ground. (b) Find the maximum height to which the 3.00-kg object rises.

 

 

58.(24S) A particle of mass m = 5.00 kg is released from point A and slides on the frictionless track . Determine (a) the particle's speed at points B and C and (b) the net work done by the gravitational force in moving the particle from A to C.

 

 

 

 

 

Friction

 

 

59.(52G) A 110-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 350 N. For the first 15 m the floor is frictionless, and for the next 15 m the coefficient of friction is 0.30. What is the final speed of the crate?

 

60.(53G) Suppose the roller coaster in Fig. 6–41 passes point 1 with a speed of  If the average force of friction is equal to one-fifth of its weight, with what speed will it reach point 2? The distance traveled is 45.0 m.

 

61.(55G) A 0.620-kg wood block is firmly attached to a very light horizontal spring  as shown in Fig. 6–40. It is noted that the block–spring system, when compressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium position before stopping and turning back. What is the coefficient of kinetic friction between the block and the table?

             

62.(31S) The coefficient of friction between the 3.00-kg block and the surface in Figure P8.31 is 0.400. The system starts from rest. What is the speed of the 5.00-kg ball when it has fallen 1.50 m?

 

63.(33S)A 5.00-kg block is set into motion up an inclined plane with an initial speed of 8.00 m/s (Fig. P8.33). The block comes to rest after traveling 3.00 m along the plane, which is inclined at an angle of 30.0° to the horizontal.  For this motion determine (a) the change in the block's kinetic energy, (b) the change in the potential energy of the block-Earth system, and (c) the friction force exerted on the block (assumed to be constant).  (d) What is the coefficient of kinetic friction?

 

64.(36S).A 50.0-kg block and 100-kg block are connected by a string as in Figure P8.36. The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between the 50-kg block and incline is 0.250. Determine the change in the kinetic energy of the 50-kg block as it moves from A to B, a distance of 20.0 m

 

65.(57S)A 10.0-kg block is released from point A in Figure P8.57. The track is frictionless except for the portion between points B and C , which has a length of 6.00 m.  The block travels down the track, hits a spring of force constant 2 250 N/m, and compresses the spring 0.300 m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between the block and the rough surface between B and C.