To determine
To find:
The work needed to stretch the spring 9 in. beyond its natural length
Answer
6.75 ft· lb
Explanation
1) Concept:
Use Hook’s law and formula of work done
2) Law and Formula:
Hook’s law:
The force required to stretch a spring x units beyond its natural length is proportional to x, and it is given by fx=kx where k is a positive constant called the spring constant.
Work done:
W=∫abf(x)dx
3) Calculation:
From the given information,
12=∫01kxdx
Simplify,
⇒12=kx2201
⇒12=k(1)22-k(0)22
⇒12=k2
⇒k=24 lb/ft
Therefore, the work required to stretch the spring 9 in = ¾ ft is
∫03/424xdx
=24x22034
=24(34)22-24(0)22
=(24)(9)(16)(2)-0
=274
=6.75 ft· lb
Conclusion:
The work needed to stretch the spring 9 in. beyond its natural length is 6.75 ft·lb