VP1. Consider the three connected objects shown in the figure below. Assume fırst that the inclined plane is frictionless and that the system is in equilibrium. In terms of m, g, and 6, find (a) the mass M and (b) the tensions T1 and T2. Now assume that the value of M is double the value found in part (a). Find (c) the acceleration of each object and (d) the tensions T, and T2. Next, assume that the coefficient of static friction between n and 2m and the inclined plane is µs and that the system is in equilibrium. Find (e) the maximum value of M and (f) the minimum value of M. (g) Compare the values of T2 when M has its minimum and maximum values. T2 T 2m M

VP1. Consider the three connected objects shown in the figure below. Assume fırst that the inclined plane is frictionless and that the system is in equilibrium. In terms of m, g, and 6, find (a) the mass M and (b) the tensions T1 and T2. Now assume that the value of M is double the value found in part (a). Find (c) the acceleration of each object and (d) the tensions T, and T2. Next, assume that the coefficient of static friction between n and 2m and the inclined plane is µs and that the system is in equilibrium. Find (e) the maximum value of M and (f) the minimum value of M. (g) Compare the values of T2 when M has its minimum and maximum values. T2 T 2m M

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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Question

Ch6 VP1

### Problem Statement
**VP1.** Consider the three connected objects shown in the figure below. Assume first that the inclined plane is frictionless and that the system is in equilibrium. In terms of \( m, g, \) and \( \theta \), find (a) the mass \( M \) and (b) the tensions \( T_1 \) and \( T_2 \). Now assume that the value of \( M \) is double the value found in part (a). Find (c) the acceleration of each object and (d) the tensions \( T_1 \) and \( T_2 \). Next, assume that the coefficient of static friction between \( m \) and \( 2m \) and the inclined plane is \( \mu_s \), and that the system is in equilibrium. Find (e) the maximum value of \( M \) and (f) the minimum value of \( M \). (g) Compare the values of \( T_2 \) when \( M \) has its minimum and maximum values.

### Diagram Explanation
The diagram depicts an inclined plane with an angle \( \theta \). There are three connected objects:

1. A mass \( 2m \) resting on the plane, with tension \( T_1 \) in the cord connecting it to another mass.
2. A mass \( m \) also on the plane, farther up, connected to the mass \( 2m \) by a cord under tension \( T_1 \), and experiencing tension \( T_2 \) in another cord going over a pulley.
3. A mass \( M \) hanging vertically, connected to the mass \( m \) via the cord with tension \( T_2 \).

This system's dynamics are governed by forces including gravitational force, tension, and potentially friction if a coefficient is provided.

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