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6. The device shown in the figure below is an example of what is known as an Atwood's machine. It consists of a mass m and a mass M joined by a string passing over a pulley. You may assume that the string and pulley are massless, that friction is negligible, and that M > m. m M (a) Using Newton's 2nd Law and the force-based approach we developed earlier in the semester, find an expression for the magnitude of the acceleration for each mass. (b) Then, use the kinematic equations for constant acceleration to find an expression for the magnitude of final velocity for each mass after they have moved through a height h. Assume that both masses start at the same height and are released from rest. (c) Use energy conservation instead to find an expression for the magnitude of final velocity for each mass after they have moved through a height h. Your result should agree with the result you found in parts (a) and (b).

6. The device shown in the figure below is an example of what is known as an Atwood's machine. It consists of a mass m and a mass M joined by a string passing over a pulley. You may assume that the string and pulley are massless, that friction is negligible, and that M > m. m M (a) Using Newton's 2nd Law and the force-based approach we developed earlier in the semester, find an expression for the magnitude of the acceleration for each mass. (b) Then, use the kinematic equations for constant acceleration to find an expression for the magnitude of final velocity for each mass after they have moved through a height h. Assume that both masses start at the same height and are released from rest. (c) Use energy conservation instead to find an expression for the magnitude of final velocity for each mass after they have moved through a height h. Your result should agree with the result you found in parts (a) and (b).

College Physics
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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**Title: Understanding Atwood's Machine** **Text:** 6. The device shown in the figure below is an example of what is known as an Atwood’s machine. It consists of a mass \( m \) and a mass \( M \) joined by a string passing over a pulley. You may assume that the string and pulley are massless, that friction is negligible, and that \( M > m \). **Diagram Explanation:** - The diagram illustrates an Atwood's machine, which comprises a pulley mounted on a horizontal support. - Two masses, \( m \) and \( M \), are suspended from either side of the pulley by a string. - The mass \( M \) is heavier than the mass \( m \), which results in the movement of the masses. **Problem:** (a) Using Newton’s 2nd Law and the force-based approach we developed earlier in the semester, find an expression for the magnitude of the acceleration for each mass. (b) Then, use the kinematic equations for constant acceleration to find an expression for the magnitude of final velocity for each mass after they have moved through a height \( h \). Assume that both masses start at the same height and are released from rest. (c) Use energy conservation instead to find an expression for the magnitude of final velocity for each mass after they have moved through a height \( h \). Your result should agree with the result you found in parts (a) and (b).
Transcribed Image Text:**Title: Understanding Atwood's Machine** **Text:** 6. The device shown in the figure below is an example of what is known as an Atwood’s machine. It consists of a mass \( m \) and a mass \( M \) joined by a string passing over a pulley. You may assume that the string and pulley are massless, that friction is negligible, and that \( M > m \). **Diagram Explanation:** - The diagram illustrates an Atwood's machine, which comprises a pulley mounted on a horizontal support. - Two masses, \( m \) and \( M \), are suspended from either side of the pulley by a string. - The mass \( M \) is heavier than the mass \( m \), which results in the movement of the masses. **Problem:** (a) Using Newton’s 2nd Law and the force-based approach we developed earlier in the semester, find an expression for the magnitude of the acceleration for each mass. (b) Then, use the kinematic equations for constant acceleration to find an expression for the magnitude of final velocity for each mass after they have moved through a height \( h \). Assume that both masses start at the same height and are released from rest. (c) Use energy conservation instead to find an expression for the magnitude of final velocity for each mass after they have moved through a height \( h \). Your result should agree with the result you found in parts (a) and (b).
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