Page 253 - Fisika Terapan for Engineers and Scientists

Problems 453

7. The plant of the foot of an average male is 26 cm, and the 10. One end of a uniform beam of mass 50 kg and length 3.0 m
height of his center of mass above the floor is 1.03 m. When rests on the ground; the other end is held above the ground by
he is standing upright, the center of mass is vertically aligned a pivot placed 1.0 m from that end (see Fig. 14.38). An 80-kg
with the ankle, 18 cm from the tip of the foot (see Fig. 14.36). man walks along the beam, from the low end toward the high
Without losing his equilibrium, how far can the man lean for- end. How far beyond the pivot can the man walk before the
ward or backward while keeping his body straight and his feet high end of the beam swings down?
stiff and immobile?

1.0 m
2.0 m

1.03 m
FIGURE 14.38 Man standing on a beam.
FIGURE 14.36
Man standing on
stiff feet. 0.18 m 11. The mast of a sailboat is held by two steel cables attached
0.26 m as shown in Fig. 14.39. The front cable has a tension of
3
5.0 10 N. The mast is 10 m high. What is the tension in
8. A 50-kg log of uniform thickness lies horizontally on the the rear cable? What force does the foot of the mast exert on
ground. the sailboat? Assume that the weight of the mast can be
(a) What vertical force must you exert on one end of the log neglected and that the foot of the mast is hinged (and there-
to barely lift this end off the ground? fore exerts no torque).
(b) If you continue to exert a purely vertical force on the end
of the log, what is the magnitude of the force required to
hold the log at an angle of 30 to the ground? At an angle
of 60 ? At an angle of 85 ?
(c) If instead you exert a force at right angles to the length of
the log, what is the magnitude of the force required to
hold the log at an angle of 30 to the ground? At an angle
of 60 ? At an angle of 85 ?
9. In an unequal-arm balance, the beam is pivoted at a point
near one end. With such a balance, large loads can be bal-
anced with small standard weights. Figure 14.37 shows such a
FIGURE 14.39 Steel cables staying a mast.
balance with an arm of 50 cm swinging on a pivot 1.0 cm
from one end. When a package of sugar is deposited in the
balance pan, equilibrium is attained with a standard mass of 12. The center of mass of a 45-kg sofa is 0.30 m above its bottom,
0.12 kg in the other pan. What is the mass of the sugar? at its lateral midpoint. You lift one end of the 2.0-m-long sofa
Neglect the masses of the pans. to a height of 1.0 m by applying a vertical force at the bottom
of one end; the other end stays on the floor without slipping.
What force do you apply? Compare this with the force you
apply when a friend lifts the other end, also to 1.0 m, so that
the weight is shared equally. Based on this, who has the easier
task when a short and a tall person share a bulky load?
13. Suppose that you lift the lid of a chest. The lid is a uniform
49 cm
1.0 cm sheet of mass 12 kg, hinged at the rear. What is the smallest
force you can apply at the front of the lid to hold it at an angle
of 30 with the horizontal? At 60 ?
14. A pole-vaulter holds a 4.5-m pole horizontally with her right
hand at one end and her left hand 1.5 m from the same end.
FIGURE 14.37 Unequal-arm balance.