Page 263 - Fisika Terapan for Engineers and Scientists

Review Problems 463

95. A beam of steel hangs from a crane by means of cables
4.0 cm
attached to the upper corners of the beam making an angle
of 60 with each other. The mass of the beam is M. Find the
tensions in the cables and the compressional force in the
beam. 16 cm
96. Sheerlegs are sometimes used to suspend loads.They consist of
two rigid beams leaning against each other, like the legs of the
letter A (see Fig. 14.72).The load is suspended by a cable from
the apex of the A. Suppose that a pair of sheerlegs, each at an
angle of 30 with the vertical, are used to suspend an automo-
bile engine of mass 400 kg. What is the compressional force in
each leg? What are the horizontal and vertical forces that each
leg exerts on the ground? Neglect the mass of the legs.
FIGURE 14.74 Pliers.

30°
F

FIGURE 14.72 Sheerlegs supporting a load.
FIGURE 14.75 Teamster pushing on a wheel.

97. A 100-kg barrel is placed on a 30 ramp (see Fig. 14.73).
What push, parallel to the ramp, must you exert against the
middle of the barrel to keep it from rolling down? Assume 100. A flagpole points horizontally from a vertical wall. The pole is
that the friction between the barrel and the ramp prevents a uniform rod of mass M and length L. In addition to the pole
slipping of the barrel; that is, the barrel would roll without mount at the wall end (which is hinged and exerts no torque),
slipping if released. the pole is supported at its far end by a straight cable; the
cable is attached to the wall a distance L 2 above the pole
mount. What is the tension in the cable? What are the mag-
nitude and direction of the force provided by the pole wall
mount?
101. A wire stretches when subjected to a tension. This means that
F the wire can be regarded as a spring.
30°
(a) Express the effective spring constant in terms of the
length of the wire, its radius, and its Young’s modulus.
FIGURE 14.73 Barrel on a ramp. (b) If a steel wire of length 2.0 m and radius 0.50 mm is to
have the same spring constant as a steel wire of length
98. Figure. 14.74 shows a pair of pliers and their dimensions. If 4.0 m, what must be the radius of the second wire?
you push against the handles of the pliers with a force of 102. If a steel rope and a nylon rope of equal lengths are to stretch
200 N from each side, what is the force that the jaws of the by equal amounts when subjected to equal tensions, what
pliers exert against each other? must be the ratio of their diameters?
99. To help his horses drag a heavy wagon up a hill, a teamster *103. A long rod of steel hangs straight down into a very deep mine
pushes forward at the top of one of the wheels (see shaft. For what length will the rod break off at the top because
Fig. 14.75). If he pushes with a force of 600 N, what forward of its own weight? The density of mild steel is 7.8 10 3
3
2
8
force does he generate on the axle of the wagon? (Hint: The kg/m , and its tensile stress for breaking is 3.8 10 N/m .
diameter of the wheel can be regarded as a lever pivoted at the
ground.)