Question

Two ramps, each with the same shape angle, and height from the base contain two different objects. One ramp has a solid sphere located at the top while the other ramp has a solid cube located at the top. The mass of the sphere is equal to the mass of the cube. The objects are released from the same height. The sphere rolls without slipping, and the cube travels without friction. After leaving the ramp, which object will travel higher? Explain?

Answer 1

When the sphere rolls down the ramp its potential energy is converted to two types of energy

1) Rotational Kinetic energy which rotates or spinn the sphere while moving down.Value is Kr = 1/2 I w2

2) Translational Kinetic energy which moves the sphere down the ramp.Vale is Kt = 1/2 m v2

Therefore for a sphere the total energy which is the potential energy is converted to Kr  and Kt

But in case of a cube falling down through a ramp its total energy which is the potential energy is fully converted to the translational energy.

Therefore,when a solid sphere and a solid cube placed in same height on idential but different ramps its potential energy is equal.Because both are in the same height.The cube reaches down first because it has more transational kinetic enegy than the sphere.A part of sphere's Potential energy is gone to Rotational energy so it has less transational energy compared to the cube.After leaving the ramp cube moves higher or faster than the sphere in idential conditon where we dont consider friction.If friction is considered cube must slow down due to more surface area affecting friction than the sphere.