Answer
a) $h =\frac{\frac{1}{2}x^2 }{mg}$
b) 185 N/m
Work Step by Step
a) We use conservation of energy to obtain:
$\frac{1}{2}kx^2 =mgh $
$h =\frac{\frac{1}{2}kx^2 }{mg}$
We want a slope of k, so we find:
$h =\frac{\frac{1}{2}x^2 }{mg}$
b) To make the best fit line, plot the value $\frac{\frac{1}{2}x^2 }{mg}$ on the x-axis and h on the y-axis using excel. Then, create a best fit line. After doing this, you should find the slope of this line (and the value of k) is 185.
