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Get Full Access to University Physics - 13 Edition - Chapter 7 - Problem 17e
Get Full Access to University Physics - 13 Edition - Chapter 7 - Problem 17e

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A spring stores potential energy U0 when it is compressed

ISBN: 9780321675460 31

Solution for problem 17E Chapter 7

University Physics | 13th Edition

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University Physics | 13th Edition

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Problem 17E

A spring stores potential energy U0 when it is compressed a distance x0 from its uncompressed length. (a) In terms of U0, how much energy does the spring store when it is compressed (i) twice as much and (ii) half as much? (b) In terms of x0, how much must the spring be compressed from its uncompressed length to store (i) twice as much energy and (ii) half as much energy?

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Solution 17E When the spring gets compressed by a distance of x , the potential energy it stores is U 0 0 , which is equal to, U = 1 K x --------------------(1) 0 2 0 This is the potential energy of a spring compressed by x . 0 a) i) when the spring gets compressed twice as much, U = 1 K x = 1K (2x ) = 1 K × 4 x 2 2 2 0 2 0 = 4U 0 The potential energy would be 4 times as before. ii) When the spring gets compressed to half as much, 1 2 1 2 1 2 U = 2 K x = 2K (0.5x 0 = 2K × 0.25 × x 0 1 = U4. 0 The potential energy stored will be U . 4 0 b) i) to get a potential energy of 2U , the compressing must be, 0 1 2 1 2 2U =0 2 K x = 2 × 2 K x0 = K x 02 If we take a suitable x which will be 2x , then, 0 1 2 1 2 1 2 2 2U =0 2 K x = 2 K (2 x 0 = 2K × 2 x 0 = K x 0 The spring must be compressed by 2times the original compression to get twice potential energy. ii) to get a potential energy of 1/2U , the compressing must be, 0 2 2 1/2U =0 2K x = 2 × 2K x 0 = K4x 02 1 If we take a suitable x which will be x0, then, 2 x 2 1/2 U = 1 K x =2 1 K ( x ) =2 1 K × ( 0) = K x 2 0 2 2 2 0 2 2 4 0 The spring must be compressed by 1 times the original compression to get half of the 2 potential energy as before.

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ISBN: 9780321675460

University Physics was written by and is associated to the ISBN: 9780321675460. The full step-by-step solution to problem: 17E from chapter: 7 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. Since the solution to 17E from 7 chapter was answered, more than 1712 students have viewed the full step-by-step answer. This full solution covers the following key subjects: much, Energy, compressed, spring, its. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. This textbook survival guide was created for the textbook: University Physics, edition: 13. The answer to “A spring stores potential energy U0 when it is compressed a distance x0 from its uncompressed length. (a) In terms of U0, how much energy does the spring store when it is compressed (i) twice as much and (ii) half as much? (b) In terms of x0, how much must the spring be compressed from its uncompressed length to store (i) twice as much energy and (ii) half as much energy?” is broken down into a number of easy to follow steps, and 71 words.

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