In Fig. 15-55, three 14000 kg ore cars are held at rest on a mine railway using
ID: 2163040 • Letter: I
Question
In Fig. 15-55, three 14000 kg ore cars are held at rest on a mine railway using a cable that is parallel to the rails, which are inclined at angle = 31. The cable stretches 17 cm just before the coupling between the two lower cars breaks, detaching the lowest car. Assuming that the cable obeys Hooke's law, find the (a) frequency and (b) amplitude of the resulting oscillations of the remaining two cars.
In Fig. 15-55, three 14000 kg ore cars are held at rest on a mine railway using a cable that is parallel to the rails, which are inclined at angle = 31½. The cable stretches 17 cm just before the coupling between the two lower cars breaks, detaching the lowest car. Assuming that the cable obeys Hooke's law, find the (a) frequency and (b) amplitude of the resulting oscillations of the remaining two cars.Explanation / Answer
m = 14000 kg
d = 0.17 m
first compute spring constant of rope:
k = 3mgsin/d = 3*14000*9.8*sin31/0.17 = 1.25*106
frequency of oscillation:
f = /2 = (1/2)(k/2m) = (1/2)(1.25*106/2*14000) = 1.06 Hz
the amplitude equals the original displacement from the equilibrium position oftwo cars on the rope:
A = mgsin/k = 14000*9.8sin31/1.25*106 = 0.058 m