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Suppose that 4 J of work is needed to stretch a spring from its natural length of 30 cm to a...

Question:

Suppose that 4 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 42 cm.

(a) How much work is needed to stretch the spring from 38 cm to 40 cm?

(b) How far beyond its natural length will a force of 10 N keep the spring stretched?

Find the Work Using Hooke's Law:

To solve this problem we will use the following theorem:

Hooke's Law : {eq}F = kx {/eq}

Where {eq}x {/eq} is the distance the spring is stretched from its natural length and {eq}k {/eq} is the spring constant.

Answer and Explanation: 1

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The spring natural length is 30 cm. So it is stretched 12 cm. or 0.12 m. from the natural length.

Now we can write:

{eq}\begin{align*} W &= \int dw...

See full answer below.


Learn more about this topic:

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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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