A high-speed lifting mechanism supports a(n) 740-kg object with a steel cable th
ID: 1466239 • Letter: A
Question
A high-speed lifting mechanism supports a(n) 740-kg object with a steel cable that is 40.0 m long and 4.00 cm2 in cross-sectional area.
(a) Determine the elongation of the cable. (Enter your answer to at least two decimal places.) ___mm
(b) By what additional amount does the cable increase in length if the object is accelerated upwards at a rate of 3.1 m/s2? ___mm
(c) What is the greatest mass that can be accelerated upward at 3.1 m/s2 if the stress in the cable is not to exceed the elastic limit of the cable, which is 2.2 108 Pa? ____kg
Explanation / Answer
the formula for Young modulus of the object
Y = FL/ A del L
del L = FL/ A Y
= mg L/ A Y
= 740( 9.8)40/ ( 4.0 * 10 ^-4 m^2) ( 20* 10 ^10)
=3.6 mm
(b)
if the object is accelerated upwards at a rate of 3.1 m/s2 the additional change
del L = FL/ A Y
= mg L/ A Y
= 740( 9.8+3.1)40/ ( 4.0 * 10 ^-4 m^2) ( 20* 10 ^10)
=4.4 mm
the additional change in length is
4.4 mm - 3.6 mm = 0.8 mm
the force acting on the cable is
F = EA
m( g+a) = E A
m = EA/ g+a
= 2.2* 10 ^8 ( 4 * 10 ^-4)/9.8 + 3.1
=6821.7 kg
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