Answer
(a) 44J (b) 44J
Work Step by Step
(a) Work from a variable force can be expressed as $$W=-\int F dx$$ Substituting in the known spring force $F=-kx$ yields a work of $$-\int -kx dx= \frac{1}{2}k\Delta x^2$$ (Use power rule to integrate.) To find the work, use the known values of $k=3.5\times 10^4N/m$ and $\Delta x=0.050m$ yields a work of $$W=\frac{1}{2}(3.5\times 10^4N/m)(0.050m)^2=44J$$ (b) The work needed to compress a spring a distance $\Delta x$ is the same as the work needed to stretch the spring $\Delta x$. Therefore, the work needed to compress the spring $0.050m$ is also equal to $44J$.
