Page 27 - Fisika Terapan for Engineers and Scientists

Problems 227

7. A record for stair climbing was achieved by a man who raced 15. A constant force of 25 N is applied to a body while it moves
up the 1600 steps of the Empire State Building to a height of along a straight path for 12 m. The force does 175 J of work
320 m in 10 min 59 s. If his average mass was 75 kg, how on the body. What is the angle between the force and the
much work did he do against gravity? At what average rate (in path of the body?
J/s) did he do this work? *16. A strong, steady wind provides a force of 150 N in a direction
8. Suppose you push on a block sliding on a table. Your push has 30 east of north on a pedestrian. If the pedestrian walks first
a magnitude of 50 N and makes a downward angle of 60 with 100 m north and then 200 m east, what is the total work done
the direction of motion. What is the work you do on the block by the wind?
while the block moves a distance of 1.6 m? *17. A man pulls a cart along a level road by means of a short rope
9. Consider the barge being pulled by two tugboats, as described stretched over his shoulder and attached to the front end of
in Example 4 of Chapter 5. The pull of the first tugboat is the cart. The friction force that opposes the motion of the cart
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2.5 10 N at 30 to the left, and the pull of the second tug- is 250 N.
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boat is 1.0 10 N at 15 to the right (see Fig. 7.26). What is (a) If the rope is attached to the cart at shoulder height, how
the work done by each tugboat on the barge while the barge much work must the man do to pull the cart 50 m at con-
moves 100 m forward (in the direction of the x axis in Fig. 7.26)? stant speed?
What is the total work done by both tugboats on the barge? (b) If the rope is attached to the cart below shoulder height
so it makes an angle of 30 with the horizontal, what is
y
the tension in the rope? How much work must the man
now do to pull the cart 50 m? Assume that enough mass
was added so the friction force is unchanged.
2.5 10 N *18. A particle moves in the x y plane from the origin x 0,
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30° y 0 to the point x 2, y 1 while under the influence of
a force F 3i 2j. How much work does this force do on the
15° particle during this motion? The distances are measured in
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meters and the force in newtons.
1.0 10 N
FIGURE 7.26 A barge pulled by two tugboats. *19. An elevator consists of an elevator cage and a counterweight
attached to the ends of a cable that runs over a pulley (Fig.
7.27). The mass of the cage (with its load) is 1200 kg, and the
10. A 2.0-kg stone thrown upward reaches a height of 4.0 m at a
mass of the counterweight is 1000 kg. The elevator is driven
horizontal distance of 6.0 m from the point of launch. What is
by an electric motor attached to the
the work done by gravity during this displacement?
pulley. Suppose that the elevator is
*11. A man pushes a heavy box up an inclined ramp making an angle initially at rest on the first floor of
of 30 with the horizontal.The mass of the box is 60 kg, and the the building and the motor makes
coefficient of kinetic friction between the box and the ramp is the elevator accelerate upward at the
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0.45. How much work must the man do to push the box to a rate of 1.5 m/s .
height of 2.5 m at constant speed? Assume that the man pushes (a) What is the tension in the part
on the box in a direction parallel to the surface of the ramp. of the cable attached to the ele-
12. The driver of a 1200-kg automobile notices that, with its gears vator cage? What is the tension
in neutral, it will roll downhill at a constant speed of 110 in the part of the cable attached
km/h on a road of slope 1:20. Draw a “free-body” diagram for to the counterweight?
the automobile, showing the force of gravity, the normal force (b) The acceleration lasts exactly
(exerted by the road), and the friction force (exerted by the 1.0 s. How much work has the
road and by air resistance). What is the magnitude of the fric- electric motor done in this 1200 kg
tion force on the automobile under these conditions? What is interval? Ignore friction forces
the work done by the friction force while the automobile trav- and ignore the mass of the
els 1.0 km down the road? pulley.
13. Driving an automobile down a slippery, steep hill, a driver (c) After the acceleration interval
brakes and skids at constant speed for 10 m. If the automobile of 1.0 s, the motor pulls the
mass is 1700 kg and the angle of slope of the hill is 25 ,how elevator upward at constant
much work does gravity do on the car during the skid? How speed until it reaches the third
much work does friction do on the car? floor, exactly 10.0 m above the 1000 kg
14. The automobile in Example 6 of Chapter 6 is traveling on a first floor. What is the total FIGURE 7.27
flat road. For a trip of length 250 km, what is the total work amount of work that the motor Elevator cage and
done against air friction when traveling at 20 m/s? At 30 m/s? has done up to this point? counterweight.