Conservation of Mechanical Energy for a Rolling Sphere

[adstroud]

I have one last question due on my physics homework that is due in a few and no one seems to understand how to do it. Please help :)


A solid sphere of mass 0.595 kg rolls without slipping along a horizontal surface with a translational speed of 5.16 m/s. It comes to an incline that makes an angle of 36 with the horizontal surface. Neglecting energy losses due to friction,

(a) what is the total energy of the rolling sphere?
Im pretty sure that this is a total of the trans. velocity and rotational velocity but I don't know how to get the rotational velocity from the information given.

(b) to what vertical height above the horizontal surface does the sphere rise on the incline?

 

[Doc Al]

(a) what is the total energy of the rolling sphere?
Im pretty sure that this is a total of the trans. velocity and rotational velocity but I don't know how to get the rotational velocity from the information given.

The key is that it rolls without slipping. That should tell you the relationship between translational and rotational velocity.

What's the rotational inertia of a solid sphere?

 

[physixguru]

this should help:

K.E= 1/2 mv^2 ( 1+ k^2/r^2)

 

[adstroud]

so what is the vertical height it goes on the incline

 

[Doc Al]

so what is the vertical height it goes on the incline

Hint: Mechanical energy is conserved.