Page 254 - Fisika Terapan for Engineers and Scientists

454 CHAPTER 14 Statics and Elasticity

The left hand applies an upward force and the right hand a 21. You want to pick up a nearly massless rectangular cardboard
downward force. If the mass of the pole is 3.0 kg, find those box by grabbing its top and side between your forefinger and
two forces. thumb (see Fig. 14.41). Show that this is impossible unless the
15. A 50-kg diving board is 3.0 m long; it is a uniform beam, coefficient of friction between your fingers and the box is at
bolted down at one end and supported from below a distance least 1.
1.0 m from the same end. A 60-kg diver stands at the other
end. Calculate the downward force at the bolted end and the
upward support force.
16. A window washer’s scaffolding is 12 m long; it is suspended
by a cable at each end. Assume that the scaffolding is a hori-
zontal uniform rod of mass 110 kg. The window washer (with
gear) has a mass of 90 kg and stands 2.0 m from one end of
the scaffolding. Find the tension in each cable.
17. A pencil is placed on an incline, and the angle of the incline is
slowly increased. At what angle will the pencil start to roll? FIGURE 14.41 Box held in a hand.
Assume the pencil has an exactly hexagonal cross section and
does not slip.
18. A 10-kg ladder is 5.0 m long and rests against a frictionless 22. A meterstick of wood of 0.40 kg is nailed to the wall at the 75-
wall, making an angle of 30 with the vertical. The coefficient cm mark. If the stick is free to rotate about the nail, what hori-
of friction between the ladder and the ground is 0.35. A 60- zontal force must you exert at the upper (short) end to deflect
kg painter begins to climb the ladder, standing vertically on the stick 30 to one side?
each rung. How far up the ladder has the painter climbed *23. A wheel of mass M and radius R is to be pulled over a step of
when the ladder begins to slip? height h, where R h. Assume that the pulling force is applied
19. Figure 14.40 shows the arrangement of wheels on a passen- at the axis of the wheel. If the pull is horizontal, what force
ger engine of the Caledonian Railway. The numbers give the must be applied to barely begin moving? If the pull at the axis is
distances between the wheels in feet and the downward instead in the direction that requires the least force to begin
forces that each wheel exerts on the track in short tons (1 moving, what force must be applied? What is the new direc-
short ton 2000 lbf; the numbers for the forces include both tion? (Hint: Consider the torques about the point of contact
the right and left wheels). From the information given, find with the step.)
how far the center of mass of the engine is behind the front *24. Consider a heavy cable of diameter d and density from which
wheel. hangs a load of mass M. What is the tension in the cable as a
20. A door made of a uniform piece of wood measures 1.0 m by function of the distance from the lower end?
2.0 m and has a mass of 18 kg. The door is entirely supported *25. Figure 14.42 shows two methods for supporting the mast of a
by two hinges, one at the bottom corner and one at the top sailboat against the lateral force exerted by the pull of the sail.
corner. Find the force (magnitude and direction) that the door In Fig. 14.42a, the shrouds (wire ropes) are led directly to the
exerts on each hinge. Assume that the vertical force on each top of the mast; in Fig. 14.42b, the shrouds are led around a
hinge is the same. rigid pair of spreaders. Suppose that the dimensions of the mast

1.7 2.4 2.3 2.3 3.6 1.7 1.4 1.7

rear front

74 74
109
117 117 117 117
153
160
FIGURE 14.40 Wheels of a locomotive.