# Suppose that 4 J of work is needed to stretch a spring from its natural length of 26 cm to a...

## Question:

Suppose that 4 J of work is needed to stretch a spring from its natural length of 26 cm to a length of 40 cm.

(a) How much work is needed to stretch the spring from 34 cm to 36 cm? (Round your answer to two decimal places.)

(b) How far beyond its natural length will a force of 40 N keep the spring stretched? (Round your answer one decimal place.)

## Spring Equation and Work Integral:

For a spring, we know that;

{eq}F = kx {/eq}

where

F is the force applied

k is the spring constant

x is displacement

Also, the work done can be obtained by:

{eq}W = \int_{a}^{b} f(x) dx\\ \therefore W = \displaystyle \frac{k\left(b^2 - a^2\right)}{2} {/eq}

where

a and b are the displacements to which the spring is stretched.

## Answer and Explanation: 1

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Given;

{eq}W = 4 J\\ x_{0} = 26 cm = 0.26 m\\ x_{1} = 40 cm = 0.4 m\\ \delta x_{1} = 0.4-0.26 =0.14 m\\ x_{2} = 34 cm = 0.34 m\\ \delta x_{2} =...

See full answer below.

#### Learn more about this topic: Hooke's Law & the Spring Constant: Definition & Equation

from

Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.