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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

Hooke’s law describes an ideal spring. Many real springs are better described by the restoring force , where q is a constant.

Consider a spring with .

It is also .

a. How much work must you do to compress this spring ? Note that, by Newton’s third law, the work you do on the spring is the negative of the work done by the spring.

b. By what percent has the cubic term increased the work over what would be needed to compress an ideal spring? Hint: Let the spring lie along the s-axis with the equilibrium position of the end of the spring at .

Then ∆s = s.

a. The work done by person is

b. The cubical term increases the work by

See the step by step solution

Step by Step Solution

Step 1: Content Introduction

The work done by force Fs , on the particle if the particle moves in the same direction as that of the force is expressed as follow:

here, is the force and is the small displacement in the direction of the force.

Step 2: Explanation (Part a)

The equation of the spring force is

Suppose the particle move from . Therefore, the work done by the person is negative the work done by spring. Therefore,


Substitute the values and evaluate W.

Step 3: Explanation (part b)


here, the second part (cubical) gives . Therefore finding the percentage of the second term from the first term

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