Answer to Question #335934 in Calculus for alli

Question

A spring exerts a force of 100 N when it is stretched 0.2 m beyond its natural length. How much work is required to stretch the spring 0.8 m. beyond its natural length?

Answer 1

F=kx

k=F/x=100/0.2=500

$W=\smallint^b_a kxdx=k\int^{0.8}_0xdx=500(x^2/2)|^{0.8}_0=500(0.8^2/2-0^2/2)=160$