Page 261 - Fisika Terapan for Engineers and Scientists

Problems 461

*82. A rod of cast iron is soldered to the upper edges of a plate of
1.0 cm copper whose lower edge is held in a vise (see Fig. 14.66). The
rod has a diameter of 4.0 cm and a length of 2.0 m. The
copper plate measures 6.0 cm 6.0 cm 1.0 cm. If we pull
the free end of the iron rod forward by 3.0 mm, what is the
shear strain ( x h) of the copper plate?
1.5 cm
2.0 m
F
4.0 cm

6.0 cm

FIGURE 14.64 A slab of stone held by bolts.
FIGURE 14.66 Iron rod and copper plate.

79. A nylon rope of diameter 1.3 cm is to be spliced to a steel *83. When a bar of steel is heated, it expands in length by
rope. If the steel rope is to have the same ultimate breaking 0.0012% for each degree Celsius of temperature increase. If
strength as the nylon, what diameter should it have? The ulti- the length of the heated bar is to be reduced to its original
2
9
mate tensile strength is 2.0 10 N/m for the steel and value, a compressive stress must be applied to it. The com-
2
8
3.2 10 N/m for nylon. pressive stress required to cancel the thermal expansion is
*80. A rod of aluminum has a diameter of 1.000002 cm. A ring of called thermal stress. What is its value for a cylindrical bar of
2
cast steel has an inner diameter of 1.000000 cm. If the rod cast steel of cross section 4.0 cm heated by 150 C?
and the ring are placed in a liquid under high pressure, at *84. A power cable of copper is stretched straight between two
what value of the pressure will the aluminum rod fit inside the fixed towers. If the temperature decreases, the cable tends to
steel ring? contract (compare Problem 83). The amount of contraction
*81. A heavy uniform beam of mass 8000 kg and length 2.0 m is for a free copper cable or rod is 0.0017% per degree Celsius.
suspended at one end by a nylon rope of diameter 2.5 cm and Estimate what temperature decrease will cause the cable to
at the other end by a steel rope of diameter 0.64 cm. The snap. Pretend that the cable obeys Eq. (14.18) until it reaches
ropes are tied together above the beam (see Fig. 14.65). The its breaking point, which for copper occurs at a tensile stress
2
8
unstretched lengths of the ropes are 3.0 m each. What angle of 2.4 10 N/m . Ignore the weight of the cable and the sag
will the beam make with the horizontal? and stress produced by the weight.
3
3
**85. A meterstick of steel, of density 7.8 10 kg/m , is made to
rotate about a perpendicular axis passing through its middle.
What is the maximum angular velocity with which the stick
can rotate if its center is to hold? Mild steel will break when
8
2
the tensile stress exceeds 3.8 10 N/m .
**86. The wall of a pipe of diameter 60 cm is constructed of a sheet
of steel of thickness 0.30 cm. The pipe is filled with water
under high pressure. What is the maximum pressure, that is,
3.0 m force per unit area, that the pipe can withstand? See Problem
85 for data on mild steel.
nylon steel **87. A hoop of aluminum of radius 40 cm is made to spin about its
axis of symmetry at high speed. The density of aluminum is
3
3
2.7 10 kg/m , and the ultimate tensile breaking strength is
7
2
7.8 10 N/m . At what angular velocity will the hoop begin
to break apart?
**88. A pipe of steel with a wall 0.40 cm thick and a diameter of
4
2
50 cm contains a liquid at a pressure of 2.0 10 N/m .
2.0 m
How much will the diameter of the pipe expand due to this
FIGURE 14.65 Beam hanging from two types of rope. pressure?