Rolling sphere and cylinder same speed from different heights

[riseofphoenix]

A group of students perform the same "Conservation of Mechanical Energy" experiment that you performed in lab by allowing a solid sphere and then a solid cylinder to roll down the ramp. The solid sphere was released from a height of 13.7 cm. From what height hcylinder should the solid cylinder be released so that it has the same speed as the solid sphere when it reaches the bottom of the ramp?


I just said "13.7 cm" but I got marked as "INCORRECT"
Does anyone know the answer?

 

[bossman27]

Hint: how is the moment of inertia of a cylinder different than that of a sphere?

 

[ehild]

The initial potential energy at the top of the ramp transforms into kinetic energy at the bottom. The kinetic energy is the sum of the translational KE and the rotational one. The rotational energy depends of the moment of inertia, which depends on the shape.

ehild

 

[riseofphoenix]

Wait what?
Can you put that in an equation?
I have no idea what you just said :(

 

[ehild]

Have you studied rotational dynamics? Do you know what rolling means?

Try to read http://www.physics.ohio-state.edu/~gan/teaching/spring99/C12.pdf. Scroll down, there is an example about rolling down an incline.

ehild