Consider a spring that does not obey Hooke’s law very faithfully. One end of the spring…
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Question “Consider a spring that does not obey Hooke’s law very faithfully. One end of the spring…”
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 xaxis with
xcomponent Fx=kx−bx2+cx3 must be applied to the free end. Here
k=100N/m, b=700N/m2, and c=12000N/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?
Answer
Answer 1
Hi,
Hope you are doing well.
Part A:
The spring is not subject to Hooke’s law, and the force is also variable. To find the amount of work required to stretch or compress the spring, we must integrate the entire range from zero to x.
The Spring stretching work is done by,
The spring for stretching was created by
Given that,

Similarly,
PART
B:
Work done to compress the spring is given
by,
Work done
for compressing is given by,
Given that,

PART
C:
We have got that work done for compressing the
spring (W_{2}) is greater than work done for stretching the
spring (W).
It is easier
to stretch the spring.
Hope this helped for your studies. Keep learning. Have a
good day.
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Answer 2
Hi,
Hope you are doing well.
Part A:
The spring is not subject to Hooke’s law, and the force is also variable. To find the amount of work required to stretch or compress the spring, we must integrate the entire range from zero to x.
The Spring stretching work is done by,
The spring for stretching was created by
Given that,

Similarly,
PART
B:
Work done to compress the spring is given
by,
Work done
for compressing is given by,
Given that,

PART
C:
We have got that work done for compressing the
spring (W_{2}) is greater than work done for stretching the
spring (W).