6.68 CALC Consider a spring that does not obey Hooke's law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with x- component Fx =kx - bx² + cx³ must be applied to the free end. Here k = 100 N/m, b = 700 N/m², and c = 12,000 N/m³. Note that x > 0 when the spring is stretched and x < 0 when it is compressed. How much work must be done (a) to stretch this spring by 0.050 m from its unstretched length? (b) To compress this spring by 0.050 m from its unstretched length? (c) Is it easier to stretch or compress this spring? Explain why in terms of the dependence of F, on x. (Many real springs behave qualitatively in the same way.)
6.68 CALC Consider a spring that does not obey Hooke's law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with x- component Fx =kx - bx² + cx³ must be applied to the free end. Here k = 100 N/m, b = 700 N/m², and c = 12,000 N/m³. Note that x > 0 when the spring is stretched and x < 0 when it is compressed. How much work must be done (a) to stretch this spring by 0.050 m from its unstretched length? (b) To compress this spring by 0.050 m from its unstretched length? (c) Is it easier to stretch or compress this spring? Explain why in terms of the dependence of F, on x. (Many real springs behave qualitatively in the same way.)
College Physics
10th Edition
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
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Chapter13: Vibrations And Waves
Section: Chapter Questions
Problem 7P: A spring 1.50 m long with force constant 475 N/m is hung from the ceiling of an elevator, and a...
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Transcribed Image Text:6.68 CALC Consider a spring that does not obey Hooke's law
very faithfully. One end of the spring is fixed. To keep the spring
stretched or compressed an amount x, a force along the x-axis with x-
component Fx =kx - bx² + cx³ must be applied to the free end. Here
k = 100 N/m, b = 700 N/m², and c = 12,000 N/m³. Note that x > 0
when the spring is stretched and x < 0 when it is compressed. How
much work must be done (a) to stretch this spring by 0.050 m from its
unstretched length? (b) To compress this spring by 0.050 m from its
unstretched length? (c) Is it easier to stretch or compress this spring?
Explain why in terms of the dependence of F, on x. (Many real springs
behave qualitatively in the same way.)
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