Question

Problem 10

Answer 1

Given information

Two inclines have the same height, h, but make different angles with the horizontal.

The same steel ball rolls without slipping down each incline.

Step-by-step explanation

Step 1.

The kinetic energy is the energy possessed by the ball due to its motion.

Rotational kinetic energy is the energy possessed by the ball due to its rotational motion.

At the bottom of the incline:

Consider the total energy be   . The total energy at the top of the incline is the sum of kinetic energy and rotational kinetic energy.

The formula to calculate the kinetic energy is given by where is the mass and is the velocity.

 

The formula to calculate the rotational kinetic energy is given by   where   is the moment of inertia  and   is the angular velocity.

Therefore,