Solution Found!
Solved: CALC Consider a spring that does not obey Hooke’s
Chapter 6, Problem 74P(choose chapter or problem)
Problem 74P
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. (a) How much work must be done to stretch this spring by 0.050 m from its unstretched length? (b) How much work must be done 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 Fx on x. (Many real springs behave qualitatively in the same way.)
Questions & Answers
QUESTION:
Problem 74P
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. (a) How much work must be done to stretch this spring by 0.050 m from its unstretched length? (b) How much work must be done 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 Fx on x. (Many real springs behave qualitatively in the same way.)
ANSWER:
Solution 74P
Introduction
The force as a function of stretch is given, we have to calculate the work done to stretch the spring.
Step 1
The work done is given by
Now the force is given by
