### Problem StatementA solid sphere (moment of inertia \( I = 0.4 mR^2 \)) with radius \( R = 0.14 \) meters starts from rest and rolls without slipping down a ramp through a vertical height of 0.74 meters. At the bottom, where it is rolling horizontally, what are its linear velocity \( v \) and its rotational velocity \( \omega \)?### Diagram DescriptionThe diagram accompanying the problem shows a solid sphere at the top of a curved ramp. The ramp descends to the right from a height \( h \) which is marked to be 0.74 meters. The radius of the sphere is indicated to be R which is specified as 0.14 meters.The diagram visually represents:- A solid sphere at rest at the top of the ramp.- A curved ramp that leads to a horizontal section.- An indication of the height \( h \) of the ramp’s starting point (0.74 meters).### Calculation HintsTo solve this problem, we apply the principles of conservation of energy and the relationship between linear and rotational motion for a rolling object.1. **Conservation of Energy:** The gravitational potential energy at the top will convert into translational and rotational kinetic energy at the bottom: \[ mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2 \] 2. **Moment of Inertia (\( I \)) for a solid sphere:** \[ I = \frac{2}{5}mR^2 \] 3. **Relationship Between Linear and Rotational Motion (For Rolling Without Slipping):** \[ v = \omega R \]By substituting the given values and relationships into the conservation of energy equation, one can solve for the linear and rotational velocities.

Write the given values with the suitable variables. R=0.14 mh=0.74 mI=0.4mR2 Here, R, h, and I are…

2. A solid sphere (I = 0.4 mR2) with radius R = 0.14m starts from rest and rolls without slipping down a ramp through a vertical height of 0.74m. At the bottom where it is rolling horizontally, what are its velocity v and its rotational velocity wo? h

2. A solid sphere (I = 0.4 mR2) with radius R = 0.14m starts from rest and rolls without slipping down a ramp through a vertical height of 0.74m. At the bottom where it is rolling horizontally, what are its velocity v and its rotational velocity wo? h

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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