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Kinetic energy of spring

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A spring of mass m is pulled such that a given instant, velocity of both of its end is v in the opposite direction. Find the kinetic energy of the spring.

I tried as
Total KE = $2(\frac{1}{2}mv^2)$

But the answer given as $\frac{1}{6}mv^2$

asked Jan 27, 2017 in Physics Problems by koolman (4,286 points)
Thanks a lot

1 Answer

1 vote
Best answer

The effective mass of a spring of real mass $m$ is $\frac13m$. The middle of the spring is stationary. So think of the spring as 2 identical smaller springs of effective mass $\frac16m$ with one end fixed and the other moving at speed $v$. The total kinetic energy is $2(\frac12(\frac16m)v^2)=\frac16mv^2$.

answered Jan 27, 2017 by sammy gerbil (28,746 points)
selected Jan 28, 2017 by koolman