If the work required to stretch a spring 1 ft beyond its natural length is 15 ft-lb, how much work is needed to stretch it 3 in. beyond its natural length?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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If the work required to stretch a spring 1 ft beyond its natural length is 15 ft-lb, how much work is needed to stretch it 3 in. beyond its natural length?
If the work required to stretch a spring 1 ft beyond its natural length is 15
ft-lb, how much work is needed to stretch it 3 in. beyond its natural length?
x ft-lb
45/19
Enhanced Feedback
Please try again. Recall Hooke's Law: The force required to maintain a
spring stretched x units beyond its natural length is proportional to x. So
AX) = kx, where k is the spring constant.
Start by setting up the integral for the work required to stretch the spring a
given distance beyond its natural length for the case where work is given.
Use this integral to find k, and use k to find the amount of work
led to
stretch the spring the given distance beyond its natural length for the case
where work is unknown. Pay attention to units.
Transcribed Image Text:If the work required to stretch a spring 1 ft beyond its natural length is 15 ft-lb, how much work is needed to stretch it 3 in. beyond its natural length? x ft-lb 45/19 Enhanced Feedback Please try again. Recall Hooke's Law: The force required to maintain a spring stretched x units beyond its natural length is proportional to x. So AX) = kx, where k is the spring constant. Start by setting up the integral for the work required to stretch the spring a given distance beyond its natural length for the case where work is given. Use this integral to find k, and use k to find the amount of work led to stretch the spring the given distance beyond its natural length for the case where work is unknown. Pay attention to units.
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