/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 A force of 250 newtons stretches... [FREE SOLUTION] | 91影视

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Chapter 7: Problem 11

A force of 250 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 20 centimeters to 50 centimeters?

Short Answer

Expert verified
First, the spring constant \( k \) is calculated from the force and the stretch as \( k = \frac{250}{0.3} \). Then the work done is found as the difference of the work for stretching the spring to 50 cm and 20 cm using the formula \( W = \frac{1}{2} k x^2 \), which simplifies to the correct answer after substituting the calculated \( k \) value.

Step by step solution

01

Calculate Spring Constant \( k \)

Using Hooke's law \[ F = kx \], where \( F \) is the force applied, \( k \) is the spring constant and \( x \) is the distance of the stretch, rearranging gives \[ k = \frac{F}{x} \]. Substituting \( F = 250 \, N \) and \( x = 30 \, cm = 0.3 \, m \) (converted from cm to m as we are using SI units), gives \( k = \frac{250}{0.3} \).
02

Calculate Work Done

The work done on stretching the spring from 20 cm to 50 cm can be found using the formula for work done \[ W = \frac{1}{2} k x^2 \]. The work done is the difference between the work done to stretch the spring to 50 cm and the work done to stretch it to 20 cm, which is \[ W = \frac{1}{2} k (50^2) - \frac{1}{2} k (20^2) \]. Substitute the calculated \( k \) value here.
03

Simplify the Expression

After substitution of \( k \), the expression should be simplified to give the final answer.

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