Explanation Given information: The required force to maintain a spring stretched from its natural length of 12 cm to 20 cm is 30 N. Apply Hooke’s Law to find the spring constant: F ( x ) = k x (1) Here, F ( x ) is force, k is spring constant, and x is amount of extension. Calculation: Calculate the spring constant using Equation (1). Substitute 30 N for F and ( 15 cm − 12 cm ) for x in Equation (1). 30 N = ( 15 cm − 12 cm ) × k = ( 3 cm × 1 m 100 cm ) × k = 0.03 k k = 30 0.03 = 1 , 000 N/m Show the expression to find the work done to stretch the spring from 12 cm to 20 cm. W = ∫ a b k x d x (2) Here, a is the lower limit and b is the upper limit. Consider that the lower limit as 0 cm. Hence, a = 0 cm Calculate the upper limit as follows: b = Stretching length − Natural length = 20 cm − 12 cm = 8 cm × 1 m 100 cm = 0

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ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

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Chapter 6, Problem 27RE

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To calculate: the work done in stretching the spring from 12 cm to 20 cm.

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the work done in stretching the spring from 12 cm to 20 cm .

Solution Summary: The author calculates the required force to maintain a spring stretched from its natural length of 12 cm to 20 cm using Hooke's Law.

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