A 20 cm long spring stretches to a length of 22cm when pulled horizontally with a force of 100N. It is placed vertically on the ground and 10.2 kg block is held 10cm above the spring. The block is dropped, hits the spring and compresses it. What is the height of the spring at the point of maximum compression?
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Answer:
F = ke, F = 100N, e = 0.02m
k = F/e = 5000N/m
compression gives stored energy
stored energy = 1/2 k e²
loss in PE = mg(0.1 + e) = gained in stored energy = 1/2 k e²
100(0.1 + e) = 2500 e²
1 + 10e = 250 e²
using formula,
e = 0.0863 or -0.0463 (reject)
compression of 8.63 cm
Height of spring = 20 - 8.63 = 11.4 cm
