# A spring has k = 88 N/m. Use a graph to determine the work needed to stretch it from x = 3.6 cm...

## Question:

A spring has {eq}k = 88\ \dfrac Nm {/eq}. Use a graph to determine the work needed to stretch it from {eq}x = 3.6\ cm {/eq} to {eq}x = 5.6\ cm {/eq}, where x is the displacement from its unstretched length.

## The Force-Extension Graph:

A spring stretched through {eq}\displaystyle {x} {/eq} from its unextended length exerts a restoring force {eq}\displaystyle {F_r} {/eq} proportional to the extension. The proportionality constant is the spring constant {eq}\displaystyle {k} {/eq}. That is {eq}\displaystyle {F_r=-kx } {/eq}. This is the Hooke's Law Force. Due to this particular form of the restoring force, the force-extension graph will be a straight line.

## Answer and Explanation: 1

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The restoring force exerted by the spring is given by the Hooke's Law as:

{eq}\displaystyle {F=-kx} {/eq}.

Here x is the displacement of the...

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#### 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.