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Chapter 11: Problem 24

A spring has a force constant of \(15.0 \mathrm{~N} / \mathrm{cm} .(a)\) How much work is required to extend the spring \(7.60 \mathrm{~mm}\) from its relaxed position? ( \(b\) ) How much work is needed to extend the spring an additional \(7.60 \mathrm{~mm}\) ?

Short Answer

Expert verified
The work required to extend the spring first 7.60 mm is \(W_1\) and the work required for another 7.60 mm is \(W_2 = W_{total} - W_1\) where the values can be obtained from the above calculations.

Step by step solution

01

Calculate work done for first extension

Use the formula \(W = 1/2 * k * X^2\) where k is the spring constant and X is the extension. Substituting the given values, we get \(W = 1/2 * 15.0 N/cm * (7.60 mm)^2).\ Convert 7.60mm to cm to match the spring constant's units, then perform the operation.
02

Calculate work done for second extension

The total work done to stretch the spring by 2* 7.60 mm would be \(W_{total} = 1/2 * k * (2*X)^2\). Compute this value. The work done for the second extension is the difference between the \(W_{total}\) and the work done for the first extension. Thus, subtract the first work value from the total work done.

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