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# If work W is required to stretch a spring a distance x ISBN: 9780321675460 31

## Solution for problem 24DQ Chapter 6

University Physics | 13th Edition

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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?

Step-by-Step Solution:

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. 2 Therefore, W = kx × x = kx Step 2: When in order to stretch the spring an additional distance of “x”, we should apply a force, F ’ = k × (x+x) = 2kx The work done would be, W ’ = F ’ × 2x = 2kx × 2x = 4kx = 4 W, (we know that, Fx = W) Therefore, in order to stretch the spring for a distance of 2x, the work done would be four times that of the work needed to stretch the spring for “x” distance.

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##### ISBN: 9780321675460

This full solution covers the following key subjects: work, distance, stretch, required, spring. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. This textbook survival guide was created for the textbook: University Physics, edition: 13. Since the solution to 24DQ from 6 chapter was answered, more than 337 students have viewed the full step-by-step answer. University Physics was written by and is associated to the ISBN: 9780321675460. The answer to “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?” is broken down into a number of easy to follow steps, and 32 words. The full step-by-step solution to problem: 24DQ from chapter: 6 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

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