Answered: Find an expression for the maximum…

Find an expression for the maximum compression of the spring d caused by mass m2 when it hits the spring. Your answer should be in terms of the variables given (and g). 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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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

The pulley system depicted consists of two masses connected by a string of negligible mass through a massless pulley. There is a spring with a constant \( k \) positioned such that its equilibrium position is located a distance \( h \) below the bottom of mass \( m_2 \). Notably, there is no friction either in the pulley or between the surfaces of the masses and the platform. When the two masses \( m_1 \) and \( m_2 \) are released from rest, mass \( m_2 \) begins to fall and pulls mass \( m_1 \) up the ramp.

### Problem Statement
Find an expression for the maximum compression of the spring \( d \) caused by mass \( m_2 \) when it hits the spring. Your answer should be in terms of the variables given (and \( g \)).

### Diagram Explanation
- The diagram shows a mass \( m_2 \) hanging vertically attached to a string over a pulley.
- Mass \( m_1 \) is resting on a ramp inclined at an angle \( \theta \).
- The spring is situated below mass \( m_2 \), with a labeled distance \( h \) indicating the initial separation.
- Arrows indicate the direction of motion for mass \( m_2 \) as it compresses the spring.

The system dynamics involve gravitational forces acting on both masses, which cause \( m_2 \) to descend, resulting in the compression of the spring upon contact.

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