Explanation The original length of the spring is 20 cm . Given: The work done to stretch a spring from 20 cm to 30 cm is W 1 . The work done to stretch the spring from 30 cm to 40 cm is W 2 . Apply Hook’s Law: The force required to maintain a spring stretched x units beyond its natural length is proportional to x . It is expressed as follows: f ( x ) = k x (1) Here, k is called spring constant. Show the expression to find the work W done to stretch the spring from a to b . W = lim n → ∞ ∑ i = 1 n f ( x i ∗ ) Δ x = ∫ a b f ( x ) d x (2) Calculation: Consider the force required to stretch the spring by x cm as f ( x ) . Consider the spring is stretched from 20 cm to 30 cm . Calculate the amount of stretch in the spring x is as shown below: x = 30 cm − 20 cm = 10 cm = 0 .1 m Consider the stretch of the spring is 0 at the beginning. Hence, a = 0 The stretch in the spring is 0.1 m after applying the force. Hence, b = 0.1 m . Calculate the work done to stretch the spring from 20 cm to 30 cm ( W 1 ) using Equation (2). Substitute 0 for a and 0.1 for b in Equation (2). W 1 = ∫ 0 0.1 f ( x ) d x (3) Modify Equation (3) using Equation (1). W 1 = ∫ 0 0.1 k x d x (4) Substitute 0.1 for x in Equation (4). W 1 = ∫ 0 0.1 k x d x = k × [ x 2 2 ] 0 0.1 = k × ( 0

8th Edition

ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

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Chapter 5.4, Problem 11E

To determine

To compare: the work done to stretch a spring (W1) from 20 to 30 cm to work done to stretch the spring (W2) from 30 to 40 cm.

To find: the relation between W1 and W2.

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To compare: the work done to stretch a spring ( W 1 ) from 20 to 30 cm to work done to stretch the spring ( W 2 ) from 30 to 40 cm. To find : the relation between W 1 and W 2 .

Solution Summary: The author compares the work done to stretch a spring (W_1) from 20 to 30 cm with the one to 40 cm.

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To compare: the work done to stretch a spring (W1) from 20 to 30 cm to work done to stretch the spring (W2) from 30 to 40 cm.

To find: the relation between W1 and W2.

Chapter 5 Solutions

To compare: the work done to stretch a spring ( W 1 ) from 20 to 30 cm to work done to stretch the spring ( W 2 ) from 30 to 40 cm. To find : the relation between W 1 and W 2 .

Solution Summary: The author compares the work done to stretch a spring (W_1) from 20 to 30 cm with the one to 40 cm.

Concept explainers

Videos

To compare: the work done to stretch a spring (W1) from 20 to 30 cm to work done to stretch the spring (W2) from 30 to 40 cm. To find: the relation between W1 and W2.

Chapter 5 Solutions

To compare: the work done to stretch a spring (W1) from 20 to 30 cm to work done to stretch the spring (W2) from 30 to 40 cm.

To find: the relation between W1 and W2.