How much sooner does the box reach the bottom of the incline than the disk?

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The applet shows the results of releasing a frictionless block and a rolling disk with equal masses from the top of identical inclined planes.

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The applet shows the same situation, but it also shows, through bar graphs that change with time, the way that the energy is transformed as the box and the disk go down the inclined plane.

Assume that the box and disk each have mass m, the top of the incline is at height h, and the angle between the incline and the ground is theta (i.e., the incline is at an angle theta above the horizontal). Also, let the radius of the disk be R.

How much sooner does the box reach the bottom of the incline than the disk?

Express your answer in terms of some or all of the variables m, h, theta, and R, as well as the acceleration due to gravity g.

Solve this physics problem

To solve this problem, we need to compare the times it takes for both the frictionless block and the rolling disk to reach the bottom of the inclined plane. Let’s break down the solution into several steps focusing on the physics involved for each object.