# Pushing on the pump of a soap dispenser compresses a small spring. When the spring is compressed...

## Question:

Pushing on the pump of a soap dispenser compresses a small spring. When the spring is compressed {eq}0.54 \, \mathrm{cm} {/eq}, its potential energy is {eq}0.0025 \, \mathrm{J} {/eq}.

(a) What is the force constant of the spring?

(b) What compression is required for the spring's potential energy to equal {eq}0.0079 \, \mathrm{J} {/eq}?

## Spring Potential Energy:

Consider an object attached to the end of a compressed spring. When this object is released, it will oscillate back and forth as the spring stretches and compresses. Where did the energy needed for this motion come from? It must have been stored as potential energy in the initial configuration of the spring.

The energy associated with a stretched or compressed spring is called spring potential energy. It is given by the formula:

{eq}U = \frac{1}{2}kx^2 {/eq}

Here k is the spring constant and x is the spring's displacement from its equilibrium (unstretched) position.

## Answer and Explanation: 1

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The answers are (a) 171 N/m and (b) 0.960 cm.

(a) The formula for spring potential energy is:

{eq}U = \frac{1}{2}kx^2 {/eq}

We have the potential...

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

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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.