How to Calculate Work on a Moving Hoop?

What is the process to calculate the work done on a moving hoop? To calculate the work done on a moving hoop, we need to consider the kinetic energy of the hoop. By using the formula for kinetic energy, we can determine the amount of work required. Let's break it down step by step.

In this scenario, we are given the mass of the hoop (m = 120 kg) and the speed of the hoop's center of mass (v = 0.220 m/s). The rotational inertia of the hoop is also provided as I = mr^2.

Step 1: Calculate the Kinetic Energy of the Hoop

First, we need to find the total kinetic energy of the hoop, which consists of both linear kinetic energy and rotational kinetic energy. The formula for kinetic energy is:

K = (1/2)mv^2 + (1/2)Iw^2

Where w is the angular velocity of the hoop. Since w = (v/r) according to the given data, the formula becomes:

K = (1/2)mv^2 + (1/2)mr^2(v/r)^2

Step 2: Find the Work Done to Stop the Hoop

When the hoop needs to be stopped, its final kinetic energy must be zero. Therefore, the work done on the hoop can be calculated as:

Work done = Kfinal - Kinitial = 0 - Initial Kinetic Energy

Substitute the values into the formula to find the work done. In the given example, the work done on the hoop to stop it is -5.808J.

By following these steps and formulas, we can accurately calculate the work done on a moving hoop. Understanding the concepts of kinetic energy and rotational inertia allows us to solve such physics problems with ease and precision.

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