Page 221 - Fisika Terapan for Engineers and Scientists

Problems 421

*24. An automobile of mass 1200 kg has four brake drums of 28. The original Ferris wheel, built by George Ferris, had a radius
6
diameter 25 cm. The brake drums are rigidly attached to the of 38 m and a mass of 1.9 10 kg. Assume that all of its
wheels of diameter 60 cm. The braking mechanism presses mass was uniformly distributed along the rim of the wheel. If
brake pads against the rim of each drum, and the friction the wheel was initially rotating at 0.050 rev/min, what con-
between the pad and the rim generates a torque that slows the stant torque had to be applied to bring it to a full stop in 30 s?
rotation of the wheel. Assume that all four wheels contribute What force exerted on the rim of the wheel would have given
equally to the braking. What torque must the brake pads exert such a torque?
2
on each drum in order to decelerate the automobile at 7.8 m/s ? 29. The pulley of an Atwood machine for the measurement of g is
If the coefficient of friction between the pad and the drum is a brass disk of mass 120 g. When using masses m 0.4500 kg
1
0.60, what normal force must the brake pad exert on the and m 0.4550 kg, an experimenter finds that the larger
k
2
rim of the drum? Ignore the masses of the wheels. mass descends 1.6 m in 8.0 s, starting from rest. What is the
*25. In one of the cylinders of an automobile engine, the gas value of g?
released by internal combustion pushes on the piston, which, 30. A hula hoop rolls down a slope of 1:10 without slipping.
in turn, pushes on the crankshaft by means of a piston rod What is the (linear) acceleration of the hoop?
(Fig. 13.32). If the crankshaft experiences a torque of 31 N m
31. A uniform cylinder rolls down a plane inclined at an angle
and if the dimensions of the crankshaft and piston rod are as
with the horizontal. Show that if the cylinder rolls without
in Fig. 13.32, what must be the force of the gas on the piston 2
slipping, the acceleration is a g sin .
3
when the crankshaft is in the horizontal position as in Fig.
13.32? Ignore friction, and ignore the masses of the piston 32. The spare wheel of a truck, accidentally released on a straight
and rod. road leading down a steep hill, rolls down the hill without slip-
F ping.The mass of the wheel is 60 kg, and its radius is 0.40 m;
the mass distribution of the wheel is approximately that of a
uniform disk. At the bottom of the hill, at a vertical distance
piston of 120 m below the point of release, the wheel slams into a
telephone booth. What is the total kinetic energy of the wheel
just before impact? How much of this kinetic energy is trans-
lational energy of the center of mass of the wheel? How much
is rotational kinetic energy about the center of mass? What is
the speed of the wheel?
15 cm 33. Galileo measured the acceleration of a sphere rolling down an

inclined plane. Suppose that, starting from rest, the sphere
takes 1.6 s to roll a distance of 3.00 m down a 20 inclined
plane. What value of g can you deduce from this?
34. A yo-yo consists of a uniform disk with a string wound around
3.8 cm the rim. The upper end of the string is held fixed. The yo-yo
crankshaft unwinds as it drops. What is its downward acceleration?
35. A man is trying to roll a barrel along a level street by pushing
FIGURE 13.32 Automobile piston and crankshaft.
forward along its top rim. At the same time another man is
pushing backward at the middle, with a force of equal magni-
tude F (see Fig. 13.33). The barrel rolls without slipping.
13.2 The Equation of Rotational Motion Which way will the barrel roll? Find the magnitude and direc-
tion of the friction force at the point of contact with the street.
26. While starting up a roulette wheel, the croupier exerts a
The barrel is a uniform cylinder of mass M and radius R.
torque of 100 N m with his hand on the spokes of the wheel.
What angular acceleration does this produce? Treat the wheel
as a disk of mass 30 kg and radius 0.25 m.
27. The center span of a revolving drawbridge consists of a uni-
form steel girder of mass 300 metric tons and length 25 m.
This girder can be regarded as a uniform thin rod. The bridge
opens by rotating about a vertical axis through its center.
What torque is required to open this bridge in 60 s? Assume
that the bridge first accelerates uniformly through an angular
interval of 45 and then the torque is reversed, so the bridge FIGURE 13.33 One man pushes horizontally at a cylinder’s
decelerates uniformly through an angular interval of 45 and top; another pushes with equal force in the opposite direction
comes to rest after rotating by 90 . at its middle. Which way does it roll?