Question

the ball is released from rest and rolls without slipping down the rough half, reaches the bottom, and then moves up the frictionless half. assuming the ball is a uniformly dense sphere, what is the ratio of the final height to the initial height?

Answer 1

The ratio of the final height to the initial height is  5:7 .

What is conservation of mechanical energy?

Gravitational potential energy and kinetic energy are the two types of energy that we have examined thus far. Mechanical energy is the total of gravitational potential energy and kinetic energy. The mechanical energy will be constant in a closed system, one in which there are no external dissipative forces at work. In other words, nothing will alter (become more or less). The Law of Conservation of Mechanical Energy is what we refer to as this.

From  conservation of mechanical energy for rough half ball

mghi= 1/2mv2 +1/2I w2

From above

v = $\sqrt{10/7ghi}$

Further due to conservation of  energy

1/2mv2 = mghf

hf/hi = 5/7

Hence,  the ratio of the final height to the initial height is  5:7 .

Learn more about conservation of mechanical energy from given link https://brainly.com/question/19969393

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