# An unstrung bow (for shooting arrows) acts like a 2750 N/m spring with a normal length of 1.75 m....

## Question:

An unstrung bow (for shooting arrows) acts like a 2,750 N/m spring with a normal length of 1.75 m. When you attach the string, you compress the bow until it is 1.15 m long. When you fully pull back on the string to prepare for firing an arrow, you compress the bow more, reducing it to 0.85 m long.

a) How much work will the fully drawn bow do on the arrow as it fires and returns to the strung length?

b) If the bow pushes on the arrow through a distance of 56 cm, how much force will the bow exert on the arrow?

## Hooke's Law

Hooke's Law relates the deformation of a spring to force applied to deform it. A deforming force that compresses the spring is considered negative, so the equation that relates the force, F, the change in the length of the spring, x, and the spring constant equal F = -kx. Since E = F x d, the equation for the energy of the compressed spring is E = {eq}kx^2 {/eq}

## Answer and Explanation:

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a) Hooke's Law relates the compression or stretching of a spring with the force exerted on the spring according to the relationship F = -kx where k is...

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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.