### Problem DescriptionA disc with a radius of 0.060 m and rotational inertia of 0.051 kg·m^2 has a rope wrapped around its parameter. The other end of the rope is holding a 0.34 kg mass. The mass is held at a height of 1.2 m above the floor. When you release the mass from rest, it causes the disc to spin and the mass to fall. How fast is the mass as it is about to strike the ground?### HintUse torque and angular acceleration, or use energy conservation to solve the problem.---This problem can be approached using principles of rotational dynamics or conservation of energy. When the mass is released, gravitational potential energy is converted into both translational kinetic energy of the mass and rotational kinetic energy of the disc. #### Using Energy Conservation1. **Potential Energy to Kinetic Energy:** Initially, the potential energy (PE) of the mass m due to its height h is: \[ PE_{initial} = mgh \] As the mass falls, this potential energy is converted into kinetic energy (KE). The kinetic energy comprises the translational kinetic energy of the mass and the rotational kinetic energy of the disc. \[ PE_{initial} = KE_{translational} + KE_{rotational} \]2. **Translational Kinetic Energy:** The translational kinetic energy of the mass m when it reaches the ground is: \[ KE_{translational} = \frac{1}{2}mv^2 \]3. **Rotational Kinetic Energy:** The rotational kinetic energy of the disc with moment of inertia I and angular velocity \(\omega\) is: \[ KE_{rotational} = \frac{1}{2}I\omega^2 \]4. **Relationships Between Linear and Angular Quantities:** The linear velocity v of the mass is related to the angular velocity \(\omega\) of the disc by: \[ v = r\omega \] Combining these equations allows us to solve for the final velocity \(v\) of the mass.5. **Energy Equation:** \[ mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\left(\frac{v}{r}\right)^2 \] Solving this equation for \(v

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A disc with radius 0.060 m and rotational inertia 0.051 kg.m^2 has a rope wrapped around its parameter. The other end of the rope is holding a O.34 kg mass. The mass is held at 1.2 m above the floor. You release the mass from rest. This causes the disc to spin and the mass to fall. How fast is the mass as it is about to strike the ground? Hint: use torque and angular acceleration or use energy conservation.

A disc with radius 0.060 m and rotational inertia 0.051 kg.m^2 has a rope wrapped around its parameter. The other end of the rope is holding a O.34 kg mass. The mass is held at 1.2 m above the floor. You release the mass from rest. This causes the disc to spin and the mass to fall. How fast is the mass as it is about to strike the ground? Hint: use torque and angular acceleration or use energy conservation.

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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