Answered: Prediction: Find an equation that…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Prediction:

Find an equation that relates the speed of the falling mass, just before it hits the bottom of its fall,
to the height it has fallen. The variables that may be involved are: the change in height of the
falling mass (Δh), moment of inertia of the disk (Idisk), the radius of the spool (rspool), the hanging
mass (mhanger), and the acceleration of gravity (g).

1) Draw two diagrams of the situation — one for the initial state (just before the hanger is
released) and one for the final state (after the mass has fallen by a height Δh). Label the
relevant quantities on your diagrams (see the ‘prediction’ section above for what the
relevant quantities might be).

2) As we have done in class, set up a conservation-of-energy problem. Write down the initial
energy (just before the hanger is released). What kind(s) of energy is/are available
initially? Then write down the final energy (after the hanging mass has fallen by a height
Δh). What kind(s) of energy is/are present now?

3) What is the relationship between the angular speed of the disk and the translational (linear)
speed of the hanger?

4) Use your answers to 2) and 3) to solve the prediction.

The diagram illustrates a mechanical setup involving a spool, disk, shaft, pulley, and mass. Here's a detailed explanation:

1. **Spool**: A cylindrical object mounted on the top of the disk, around which a string or cable is wound.

2. **Disk**: A large, flat, circular surface connected to the shaft. It presumably rotates with the spool.

3. **Shaft**: A vertical rod or support that holds the disk and spool in place, allowing them to rotate.

4. **Pulley**: A wheel located to the right of the spool. The string or cable runs over the pulley, which changes the direction of the force applied to the mass.

5. **Mass**: An object attached to the end of the string or cable. The mass hangs vertically due to gravity, exerting a force that causes the spool and disk to rotate.

This setup is commonly used in physics experiments to study rotational motion, forces, and torque. The rotation of the disk due to the falling mass illustrates principles of mechanics, such as inertia and angular momentum.

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