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Question

By what fraction does the mass of a spring change when it is compressed by 1 cm? The mass of the spring is 200 g at its natural length and the spring constant is 500 N m1

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Solution

Given : x=1 cm =0.01 m mo=0.2 kg
Using energy conservation : P.Ei+K.Ei=P.Ef+K.Ef
12kx2+0=0+12mov2 v=kmox
v=5000.2×0.01=0.5 m/s
Mass of the boy while running m=mo1(v2c2)2
Fractional increase in the mass Δmmo=mo1(v/c)2momo=[1(v/c)2]1/21
Δmmo=1+v22c21=v22c2 (for v<<c)

Δmmo=(0.5)22×(3×108)2=1.4×1018 kg

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