Work energy and power

[koolman]

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

[swansont]

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

[koolman]

Can you tell me how

[swansont]

Can you tell me how

 

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

 

 

http://mathcentral.uregina.ca/QQ/database/QQ.09.00/esther2.html