Solved: If work W is required to stretch a spring a

Chapter 6, Problem 24DQ

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QUESTION:

 Problem 24DQ

If work W is required to stretch a spring a distance x from its unstretched length, what work (in terms of W) is required to stretch the spring an additional distance x?

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QUESTION:

 Problem 24DQ

If work W is required to stretch a spring a distance x from its unstretched length, what work (in terms of W) is required to stretch the spring an additional distance x?

ANSWER:

Solution 24DQ

Step 1:

Consider a spring having spring constant, “k” is stretched to a distance “x” from its initial length “l”. Then, the restoring force is,

F = - k x

The work done would be, W = F x

We should consider the magnitude of the force while calculating the work done because, the restoring force and force applied is having equal magnitude.

Therefore, W = kx × x = kx2

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