   Chapter 5, Problem 84AP

Chapter
Section
Textbook Problem

A cat plays with a toy mouse suspended from a light string of length 1.25 m, rapidly batting the mouse so that it acquires a speed of 2.75 m/s while the string is still vertical. Use energy conservation to find the mouse’s maximum height above its original position. (Assume the string always remains taut.)

To determine
The maximum height of mouse above its original position.

Explanation

Given Info:

The length of the string is 1.25m .

The acquired speed of the rattle toy is 2.75m/s while the string is vertical.

Since, no non-conservative force is doing work on the rat toy, the mechanical energy is conserved.

Thus,

KEi+PEi=KEf+PEf

Consider the initial height of the toy as yi=0 and the maximum height as yf .

When the toy reaches the maximum height, the kinetic energy of the toy is zero.

Formula to calculate the maximum height of the mouse is,

12mvi2+0=0+mgyf

• yf is the maximum height of the mouse
• vi is the init

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