Suppose that 3 J of work is needed to stretch a spring from its natural length of 36 cm to a...

Question:

Suppose that 3 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 49 cm.

a) How much work is needed to stretch the spring from 40 cm to 45 cm?

b) How far beyond its natural length will a force of 25 N keep the spring stretched?

Hooke's Law:

Recall that Hooke's Law tells us that the force needed to compress or stretch a spring beyond its equilibrium point is proportional to the displacment:

{eq}\begin{align*} F &= kx \end{align*} {/eq}

Recall also that work is the amount of energy needed to move something from one place to another, and is computed by integrating force over displacement:

{eq}\begin{align*} W &= \int F\ dx \end{align*} {/eq}

Answer and Explanation:

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First note that to keep our units straight, we want to make sure that we are measuring lengths in meters. The natural length is 36 cm, so to get it to...

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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.


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