   Chapter 5, Problem 24P

Chapter
Section
Textbook Problem

Two blocks are connected by a light string that passes over two frictionless pulleys as in Figure P5.24. The block of mass m2 is attached to a spring of force constant k and m1 > m2. If the system is released from rest, and the spring is initially not stretched or compressed, find an expression for the maximum displacement d of m2. Figure P5.24

To determine
The expression for maximum displacement d, of mass m2 .

Explanation

Given Info:

Force constant of spring is k .

The mass m1 is greater than m2 .

In the system, the forces doing work are gravitational force and the spring force. Both are conservative forces.

For a conservative force the total energy will be a constant.

The system is initially at rest and after the maximum upward displacement of the mass m2 , the system is again at rest. Thus, for initial and final states of the system; the kinetic energy is zero.

Since, the total energy of the system is a constant; the gravitational potential energy given by the mass m1 will be equal to the sum of the elastic potential energy stored in the spring when it is stretched a distance d and the gravitational potential energy gained by the mass m2 when it go up a distance d.

Therefore,

m1g|d|=m2g|d|+12k|d<

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