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Get Full Access to University Physics - 13 Edition - Chapter 7 - Problem 14e
Get Full Access to University Physics - 13 Edition - Chapter 7 - Problem 14e

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# An ideal spring of negligible mass is 12.00 cm long when ISBN: 9780321675460 31

## Solution for problem 14E Chapter 7

University Physics | 13th Edition

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Problem 14E

An ideal spring of negligible mass is 12.00 cm long when nothing is attached to it. When you hang a 3.15-kg weight from it, you measure its length to be 13.40 cm. If you wanted to store 10.0 J of potential energy in this spring, what would be its ?total? length? Assume that it continues to obey Hooke’s law.

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Solution 14E Hooke’s law is given by F = kx, where k is the force constant of a spring and x is its elongation. When the 3.15 kg weight is hung from the spring, its length changes by x = 13.40 12.00 cm = 1.40 cm = 0.014 m Now, the force needed to extend the spring will be balanced by the weight of the object, So, mg = kx k = mg/x k = 3.15 × 9.8 N/0.014 m = 2205 N/m Now, the potential energy of a spring with force constant k and elongation x is given by, 1 2 P = k2 …..(1) Given that, P = 10.0 J From equation (1), 1 2 10.0 J = 2 × 2205 N/m × x x = 2205m 2 x = 0.009 m 2 x = 0.095 m x = 9.5 cm Initial length of the spring is = 12.00 cm Total length of the spring afterward = 12.00 + 9.5 cm = 21.5 cm Thus, the total length of the spring after the elongation is 21.5 cm.

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Step 3 of 3

##### ISBN: 9780321675460

The full step-by-step solution to problem: 14E from chapter: 7 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. This textbook survival guide was created for the textbook: University Physics, edition: 13. University Physics was written by and is associated to the ISBN: 9780321675460. The answer to “An ideal spring of negligible mass is 12.00 cm long when nothing is attached to it. When you hang a 3.15-kg weight from it, you measure its length to be 13.40 cm. If you wanted to store 10.0 J of potential energy in this spring, what would be its ?total? length? Assume that it continues to obey Hooke’s law.” is broken down into a number of easy to follow steps, and 59 words. Since the solution to 14E from 7 chapter was answered, more than 1064 students have viewed the full step-by-step answer. This full solution covers the following key subjects: its, spring, length, long, hang. This expansive textbook survival guide covers 26 chapters, and 2929 solutions.

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