A spring is hung from the ceiling. A 0.392 -kg block is then attached to the fre

Question

A spring is hung from the ceiling. A 0.392 -kg block is then attached to the free end of the spring. When released from rest, the block drops 0.155 m before momentarily coming to rest, after which it moves back upward. (a) What is the spring constant of the spring? (b) Find the angular frequency of the block's vibrations. Two stretched cables both experience the same stress. The first cable has a radius of 3.5x10-3 m, and is subject to a stretching force of 310 N. The radius of the second cable is 5.1x10-3 m. Determine the stretching force on the second cable.

Explanation / Answer

a) At rest, the block has PE.
At the bottom, the spring has U.
mgh = ½kh²
0.392kg * 9.8m/s² * 0.155m = ½ * k * (0.155m)²
k = 49.56 N/m

b) = (k/m) = (49.56N/m / 0.392kg) = 11.24 rad/s

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