Page 32 - Fisika Terapan for Engineers and Scientists

232 CHAPTER 7 Work and Energy

**77. You are to design a roller coaster in which cars start from rest **78. One portion of the track of a toy roller coaster is bent into a
at a height h 30 m, roll down into a valley, and then up a full vertical circle of radius R. A small cart rolling on the
mountain (Fig. 7.35). track entersthe bottom of the circle with a speed 22gR . Show
(a) What is the speed of the cars at the bottom of the valley? that this cart will fall off the track before it reaches the top of
the circle, and find the (angular) position at which the cart
(b) If the passengers are to feel 8g at the bottom of the
loses contact with the track.
valley, what must be the radius R of the arc of the circle
that fits the bottom of the valley? **79. A particle initially sits on top of a large, smooth sphere of
radius R (Fig. 7.36). The particle begins to slide down the
(c) The top of the next mountain is an arc of a circle of the
sphere, without friction. At what angular position will the
same radius R. If the passengers are to feel 0g at the top of
particle lose contact with the surface of the sphere? Where
this mountain, what must be its height h ?
will the particle land on the ground?

h
R h' R q
R

FIGURE 7.35 Profile of a roller coaster.

FIGURE 7.36 Particle sliding down a sphere.

REVIEW PROBLEMS

80. An apple falls down 35 m from the fifth floor of an apartment (b) What is the friction force of the road on the wheels, and
building to the street. The mass of the apple is 0.20 kg. How what is the amount of work that this friction force does
much work does gravity do on the apple during this fall? during the stopping process?
81. A woman pulls a sled by a rope. The rope makes an upward *86. A golf ball of mass 50 g released from a a height of 1.5 m
angle of 45 with the ground, and the woman exerts a pull of above a concrete floor bounces back to a height of 1.0 m.
150 N on the rope. How much work does the woman do if she (a) What is the kinetic energy of the ball just before contact
pulls this sled 20 m? with the floor begins? Ignore air friction.
82. A man pushes a crate along a flat concrete floor.The mass of the (b) What is the kinetic energy of the ball just after contact
crate is 120 kg, and the coefficient of friction between the crate with the floor ends?
and the floor is 0.50. How much work does the man do if, (c) What is the loss of energy during contact with the floor?
k
pushing horizontally, he moves the crate 15 m at constant speed?
87. A small aircraft of mass 1200 kg is cruising at 250 km/h at an
83. A 1500-kg automobile is traveling at 20 m/s on a level road.
altitude of 2000 m.
How much work must be done on the automobile to acceler-
(a) What is the gravitational potential energy (relative to the
ate it from 20 m/s to 25 m/s? From 25 m/s to 30 m/s?
ground), and what is the kinetic energy of the aircraft?
84. A woman slowly lifts a 20-kg package of books from the floor
(b) If the pilot puts the aircraft into a dive, what will be the
to a height of 1.8 m, and then slowly returns it to the floor.
gravitational potential energy, what will be the kinetic
How much work does she do on the package while lifting?
energy, and what will be the speed when the aircraft
How much work does she do on the package while lowering?
reaches an altitude of 1500 m? Assume that the engine of
What is the total work she does on the package? For the
the aircraft compensates the friction force of air, so the
information given, can you tell how much work she expends
aircraft is effectively in free fall.
internally in her muscles, that is, how many calories she expends?
88. In a roller coaster, a car starts from rest on the top of a 30-m-
85. An automobile of 1200 kg is traveling at 25 m/s when the
high mountain. It rolls down into a valley, and then up a 20-
driver suddenly applies the brakes so as to lock the wheels and
m-high mountain. What is the speed of the car at the bottom
cause the automobile to skid to a stop. The coefficient of
of the valley, at ground level? What is the speed of the car at
sliding friction between the tires and the road is 0.90.
the top of the second mountain?
(a) What is the deceleration of the automobile, and what is
the stopping distance?