**Problem Statement:** Three masses are hanging from frictionless pulleys and reach static equilibrium as shown in the figure. Assume $ m_1 = 30.0 \, \text{g} $, $ \theta_a = 120.0^\circ $, and $ \theta_b = 160.0^\circ $. Determine (a) $ m_2 $ and (b) $ m_3 $ value. Use the component method. **Diagram Explanation:** The diagram shows a system with three masses connected by strings. The strings pass over pulleys that are positioned at the top corners of the setup. Here's a breakdown of the components: - **String 1** connects mass $ m_1 $ to a knot where all strings meet. It creates an angle $ \theta_a = 120.0^\circ $ with the horizontal, extending towards the left pulley. - **String 2** is vertical and holds mass $ m_2 $ beneath the knot. - **String 3** connects the knot to mass $ m_3 $, extending towards the right pulley and making an angle $ \theta_b = 160.0^\circ $ with the horizontal. Static equilibrium means the vector sum of the forces acting on the knot is zero. This requires breaking down the tensions into horizontal and vertical components and setting up equations to solve for the unknown masses $ m_2 $ and $ m_3 $.

Problem Statement: Three masses are hanging from frictionless pulleys and reach static equilibrium as shown in the figure. Assume $ m_1 = 30.0 \, \text{g} $, $ \theta_a = 120.0^\circ $, and $ \theta_b = 160.0^\circ $. Determine (a) $ m_2 $ and (b) $ m_3 $ value. Use the component method. Diagram Explanation: The diagram shows a system with three masses connected by strings. The strings pass over pulleys that are positioned at the top corners of the setup. Here's a breakdown of the components: - String 1 connects mass $ m_1 $ to a knot where all strings meet. It creates an angle $ \theta_a = 120.0^\circ $ with the horizontal, extending towards the left pulley. - String 2 is vertical and holds mass $ m_2 $ beneath the knot. - String 3 connects the knot to mass $ m_3 $, extending towards the right pulley and making an angle $ \theta_b = 160.0^\circ $ with the horizontal. Static equilibrium means the vector sum of the forces acting on the knot is zero. This requires breaking down the tensions into horizontal and vertical components and setting up equations to solve for the unknown masses $ m_2 $ and $ m_3 $.

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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