Page 260 - Fisika Terapan for Engineers and Scientists

460 CHAPTER 14 Statics and Elasticity

*64. A scissors jack has the dimensions shown in Fig. 14.62. The lower end. By how much does this wire stretch in excess of its
screw of the jack has a pitch of 5.0 mm (as stated in the previ- initial length?
ous problem, this is the distance the screw advances when 68. An elastic cord is 5.0 m long and 1.0 cm in diameter and acts
given one full turn). Suppose the scissors jack is partially as a spring with spring constant 70 N/m. What is the Young’s
extended, with an angle of 55 between its upper sides. What modulus for this material?
is the mechanical advantage provided by the jack?
69. The piano wire described in Problem 67 can be regarded as a
55° spring. What is the effective spring constant of this spring?
70. A simple hand-operated hydraulic press can generate a pres-
25 cm 9 2
sure of 6.0 10 N/m . If the system is used to compress a
small volume of steel, what fraction of the original volume
does the final volume of steel occupy?
71. A 10-m length of 1.0-mm-radius copper wire is stretched by
holding one end fixed and pulling on the other end with a
18 cm force of 150 N. What is the change of length? By briefly
increasing the force to exceed the limit of elastic behavior
(a fractional elongation of approximately 1.0%), the wire may
be permanently deformed; this is often done in order to
straighten out bends or kinks in a wire. Approximately what
FIGURE 14.62 Scissors jack. force is necessary?
72. A 0.50-mm-radius fishing line made of nylon is 100 m long
**65. Figure 14.63 shows a tensioning device used to tighten the when no forces are applied. A fish is hooked and pulls with a
rear stay of the mast of a sailboat. The block and tackle pulls tension force of 250 N. What is the elongation?
down a rigid bar with two rollers that squeeze together the
73. In a skyscraper, an elevator is suspended from three equal,
two branches of the split rear stay. If the angles are as given in
parallel 300-m-long steel cables, each of diameter 1.0 cm.
the figure, what is the mechanical advantage?
How much do these cables stretch if the mass of the elevator
is 1000 kg?
74. The length of the femur (thighbone) of a woman is 38 cm,
2
F' and the average cross section is 10 cm . How much will the
femur be compressed in length if the woman lifts another
woman of 68 kg and carries her piggyback? Assume that,
momentarily, all of the weight rests on one leg.
35°
75. If the volume of a sphere subjected to an external pressure
shrinks by 0.10%, what is the percent shrinkage of the radius?
In general, show that the percent shrinkage of the volume
15° equals three times the percent shrinkage of the radius, pro-
vided the shrinkage is small.
76. At the bottom of the Marianas Trench in the Pacific Ocean,
8
2
at a depth of 10900 m, the pressure is 1.24 10 N/m .
F What is the percent increase of the density of water at this
depth as compared with the density at the surface?
77. A slab of stone of mass 1200 kg is attached to the wall of a
building by two bolts of iron of diameter 1.5 cm (see
FIGURE 14.63 Tensioning device. Fig. 14.64). The distance between the wall and the slab of
stone is 1.0 cm. Calculate by how much the bolts will sag
14.4 Elasticity of Materials downward because of the shear stress they are subjected to.
78. According to (somewhat oversimplified) theoretical consider-
66. The anchor rope of a sailboat is a nylon rope of length 60 m ations, the Young’s modulus, the shear modulus, and the bulk
and diameter 1.3 cm. While anchored during a storm, the modulus are related by
sailboat momentarily pulls on this rope with a force of 1.8 9BS
4
10 N. How much does the rope stretch? Y
3B S
67. A piano wire of steel of length 1.8 m and radius 0.30 mm is
subjected to a tension of 70 N by a weight attached to its Check this for the first four materials listed in Table 14.1.