**Problem Description:**Given:- Mass \( m_1 = 4.5 \, \text{kg} \)- No friction between \( m_2 \) and the rampObjective: Determine the mass \( m_2 \) such that the acceleration of the blocks is zero.**Diagram Explanation:**- The diagram shows a right triangle representing an inclined plane with a \( 22^\circ \) angle to the horizontal.- Block \( m_2 \) is placed on the inclined plane, and it is connected via a pulley system to block \( m_1 \), which hangs vertically.- The pulley is depicted as a circle at the top of the ramp, indicating that the weight of \( m_1 \) might affect the tension and equilibrium of the system.**Conceptual Analysis:**- To have zero acceleration, the forces on \( m_1 \) and \( m_2 \) must be balanced.- For \( m_1 \), the force due to gravity (\( m_1g \)) must be equal to the tension in the cable.- For \( m_2 \), the component of gravitational force down the incline (\( m_2g \sin(22^\circ) \)) must match the tension in the cable.Use these equations:1. \( m_1g = m_2g \sin(22^\circ) \)2. Solve for \( m_2 \) in terms of \( m_1 \).**Learning Focus:**This problem addresses concepts in physics such as:- Equilibrium of forces- Dynamics on an inclined plane- Application of trigonometry to resolve forcesBy manipulating these principles, students can better understand how forces interact in systems involving pulleys and inclines.

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Description: **Problem Description:**Given:- Mass \( m_1 = 4.5 \, \text{kg} \)- No friction between \( m_2 \) and the rampObjective: Determine the mass \( m_2 \) such that the acceleration of the blocks is zero.**Diagram Explanation:**- The diagram shows a right

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Answered: Suppose m1 = 4.5 kg and there is no…

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Suppose m1 = 4.5 kg and there is no friction between m2 and the ramp. What would the mass m2 have to be in order for the acceleration of the blocks to be zero?

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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Concept explainers

Newton's Second Law

Newton’s laws of motion describe the relationship between the motion of an object and forces acting on it. Newton’s law of motion has two types as follows:

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Question

**Problem Description:**

Given:
- Mass \( m_1 = 4.5 \, \text{kg} \)
- No friction between \( m_2 \) and the ramp

Objective: Determine the mass \( m_2 \) such that the acceleration of the blocks is zero.

**Diagram Explanation:**

- The diagram shows a right triangle representing an inclined plane with a \( 22^\circ \) angle to the horizontal.
- Block \( m_2 \) is placed on the inclined plane, and it is connected via a pulley system to block \( m_1 \), which hangs vertically.
- The pulley is depicted as a circle at the top of the ramp, indicating that the weight of \( m_1 \) might affect the tension and equilibrium of the system.

**Conceptual Analysis:**

- To have zero acceleration, the forces on \( m_1 \) and \( m_2 \) must be balanced.
- For \( m_1 \), the force due to gravity (\( m_1g \)) must be equal to the tension in the cable.
- For \( m_2 \), the component of gravitational force down the incline (\( m_2g \sin(22^\circ) \)) must match the tension in the cable.

Use these equations:
1. \( m_1g = m_2g \sin(22^\circ) \)
2. Solve for \( m_2 \) in terms of \( m_1 \).

**Learning Focus:**

This problem addresses concepts in physics such as:
- Equilibrium of forces
- Dynamics on an inclined plane
- Application of trigonometry to resolve forces

By manipulating these principles, students can better understand how forces interact in systems involving pulleys and inclines.

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