Finding the work done in stretching or compressing a spring.
Hooke's Law for Springs.
According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x)=kxF(x)=kx, for some constant kk. The value of kk (measured in force units per unit length) depends on the physical characteristics of the spring. The constant kk is called the spring constant and is always positive.
In this problem we assume that the force applied doesn't distort the metal in the spring.
Part 1.
A 3 m3 m spring requires 9 J9 J to stretch to 3.1 m3.1 m.
Find the force function, F(x)F(x), for the spring described.
F(x)= ??????????
Note: enter your answer using values correct to three decimal places.
Part 2.
How much work is required to stretch the spring to 3.4 m3.4 m?
W= ??????? J.
Note: enter your answer using values correct to three decimal places.