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

Lets find the kinetic energy of half of the spring. Its velocity changes from zero at center to v of its end.

The average velocity of half of the spring is v/2 .

The kinetic energy of half of the spring is 1/2 (m/2)(v/2)^2

The kinetic energy of the spring is (m/2)(v/2)^2

Hence my ans is mv^2/8

But ans is mv^2/6

Do you want to find the average speed, or the average of the square of the speed, in order to find the energy?

Can you tell me how

Can you tell me how

 

How do you normally find the average of a continuous function?

 

 

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