Question

ormal Frictioi X. Weight

Assume that a ball rolls down a ramp with friction without slipping. All of the sources says that the total mechanical enegry is conserved: mgH = 1/2mv^2 + 1/2Iw^2. But shouldn't the force of friction decrease the total mechanical energy here. I would expect something linke mgH - Ffrictionx = 1/2mv^2 + 1/2Iw^2.

Answer 1

Yes, due to friction the mechanical energy will not be conserved and hence the angular velocity (w) and the translational velocity (v) will be less than the ones where there is no friction.

The work done to overcome friction should also be considered as friction is a non-conservative force (dissipative force).

mgH - Ffrictionx = 1/2mv^2 + 1/2Iw^2 is correct where there is friction.