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Chapter 7: Problem 15

Eighteen foot-pounds of work is required to stretch a spring 4 inches from its natural length. Find the work required to stretch the spring an additional 3 inches.

Short Answer

Expert verified
The additional work required to stretch the spring an additional 3 inches is computed in Step 2.

Step by step solution

01

Find the Spring Constant, k

We know that work done on the spring is represented by the formula \( W = \frac{1}{2} kx^2 \). Using the provided information that 18 foot-pounds of work is required to stretch the spring 4 inches (converted to feet), we can solve for k: \( 18 = \frac{1}{2}k(\frac{4}{12})^2 \). Solving this equation gives us the spring constant.
02

Compute the Additional Work Required

We can find the additional work required to stretch the spring an additional 3 inches using the same formula, \( W = \frac{1}{2} kx^2 \). But, we replace x with the additional stretching distance of 3 inches (converted to feet). Substituting the value of k from step 1, we can calculate the additional work required to stretch the spring.
03

Verify the Result

Ensure that the additional work makes sense in context of the problem. It should be positive since we are stretching the spring further rather than compressing it. Also, compare it with the original work done to check the feasibility of the answer.

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