A manufacturer wants to build a spring that takes a force 10 N (in negative direction) to compress it 0.2 m from the equilibrium position. The spring should be able to stretch 0.5 m from the equilibrium position.
As a mechanical engineer, you were asked to present how much work should be done to stretch the spring.The presentation shall include important components of the problem, complete and correct computations and a logical and organized explanation.
Hints:
First, create a force function F(x) by finding the spring constant k in F(x) = kx where F(x) is the force and x is the position from the equilibrium.
Then, calculate work ustng the concept of the definite integral.
If a variable force F(x) moves an object in a positive direction along the x-axis from point a to point b, then the work done on the object is W = ∫ ^b a F(x) dx
The restoration force on the spring was f(x)=kx
Then small work done in streching the spring throghh length dx-
Then Total work done in streching the spring from 0.2 to 0.5m-
The spring constant
Eqn.(1)
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