**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**

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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?

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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 10^{5 } 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 m^{3}/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

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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/s^{2
} 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.

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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.

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**

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37.**(12S)
The force acting on a particle is *F _{x}* = (8

**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 = *
ò**F×***d***r **
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,

*v*^{2}
= **v·v**.)

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.

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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**

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**4****7(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?

**4****9.(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?

**5****0.(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?

**5****1.(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?

**
**

**5****3.(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 10^{4} how
far does he depress it?

**5****4.(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?

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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.

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**
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*.*

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**
Friction**

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**

**
**

**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?

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**
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?

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**
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

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**
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.

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