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December 20, 2014

December 20, 2014

Posted by **Kyle** on Monday, November 3, 2008 at 9:32am.

Do you use the equation for total mechanical energy and if so how do you get the mass and radius?

- Physics -
**Count Iblis**, Monday, November 3, 2008 at 10:20amWhat happens is that in the answer the mass and the radius drops out.

The total kinetic energy is:

Ekin = 1/2 m v^2 + 1/2 I omega^2

If the ball rolls without slipping, then:

omega = v/R

The moment of intertial of the ball is:

I = 2/5 m R^2

So, the kinetic energy is:

Ekin = 1/2 m v^2 + 1/5 m v^2 =

7/10 m v^2

The potential energy is mgh, so the total energy of the ball is at height h and velocity v is

E(h,v) = m g h + 7/10 m v^2 =

m [g h + 7/10 v^2]

The total energy is conserved, so you can find the velocity at the top by solving:

E(h=0.76 meter, v ) = E(0, v = 5.40 m/)

The unknown mass m drops out.

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