Page 256 - Fisika Terapan for Engineers and Scientists

456 CHAPTER 14 Statics and Elasticity

*31. Consider the ladder leaning against a wall described in number of books, what would be the limiting maximum pro-
Example 4. If the ladder makes an angle of 30 with the wall, trusion? (Hint: Try this experimentally; start with the top
how hard can you push down vertically on the top of the book, and insert the others underneath, one by one.)
ladder with your hand before slipping begins? **36. A wooden box, filled with a material of uniform density,
*32. An automobile with a wheelbase (distance from the front stands on a concrete floor. The box has a mass of 75 kg and is
wheels to the rear wheels) of 3.0 m has its center of mass at a 0.50 m wide, 0.50 m long, and 1.5 m high. The coefficient of
point midway between the wheels at a height of 0.65 m above friction between the box and the floor is 0.80. If you
s
the road. When the automobile is on a level road, the force exert a (sufficiently strong) horizontal push against the side of
with which each wheel presses on the road is 3100 N. What is the box, it will either topple over or start sliding without top-
the normal force with which each wheel presses on the road pling over, depending on how high above the level of the floor
when the automobile is standing on a steep road of slope 3:10 you push. What is the maximum height at which you can
with all the wheels locked? push if you want the box to slide? What is the magnitude of
*33. A wooden box is filled with material of uniform density. The the force you must exert to start the sliding?
box (with its contents) has a mass of 80 kg; it is 0.60 m wide, *37. The left and right wheels of an automobile are separated by a
0.60 m deep, and 1.2 m high. The box stands on a level floor. transverse distance of l 1.5 m. The center of mass of this
By pushing against the box, you can tilt it over (Fig. 14.48). automobile is h 0.60 m above the ground. If the automobile
Assume that when you do this, one edge of the box remains in is driven around a flat (no banking) curve of radius R 25 m
contact with the floor without sliding. with an excessive speed, it will topple over sideways. What is
(a) Plot the gravitational potential energy of the box as a the speed at which it will begin to topple? Express your
function of the angle between the bottom of the box and answer in terms of l, h, and R; then evaluate numerically.
the floor. Assume that the wheels do not skid.
(b) What is the critical angle beyond which the box will *38. An automobile has a wheelbase (distance from front wheels to
topple over when released? rear wheels) of 3.0 m. The center of mass of this automobile is
at a height of 0.60 m above the ground. Suppose that this
(c) How much work must you do to push the box to this crit-
automobile has rear-wheel drive and that it is accelerating
ical angle? 2
along a level road at 6.0 m/s . When the automobile is
F parked, 50% of its weight rests on the front wheels and 50%
on the rear wheels. What is the weight distribution when it is
accelerating? Pretend that the body of the automobile remains
parallel to the road at all times.
FIGURE 14.48 *39. Consider a bicycle with only a front-wheel brake. During
Tilted box. braking, what is the maximum deceleration that this bicycle
can withstand without flipping over its front wheel? The
center of mass of the bicycle with rider is 95 cm above the
*34. A meterstick of mass M hangs from a 1.5-m string tied to the road and 70 cm behind the point of contact of the front wheel
meterstick at the 80-cm mark. If you push the bottom end of with the ground.
the meterstick to one side with a horizontal push of magni-
*40. A bicycle and its rider are traveling around a curve of radius
tude Mg 2, what will be the equilibrium angles of the meter-
6.0 m at a constant speed of 20 km/h. What is the angle at
stick and the string?
which the rider must lean the bicycle toward the center of the
*35. Five identical books are to be stacked one on top of the other. curve (see Fig. 14.50)?
Each book is to be shifted sideways by some variable amount,
so as to form a curved leaning tower with maximum protru-
sion (see Fig. 14.49). How much must each book be shifted?
What is the maximum protrusion? If you had an infinite

FIGURE 14.49 A stack of books. FIGURE 14.50 Bicycle traveling around curve.