## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

(a) $h = \frac{k~(\Delta x)^2}{2mg}$ (b) The ice cube goes up to a height of 0.26 m
(a) The block's potential energy at the maximum height will be equal to the initial energy stored in the spring. We can find an expression for the maximum height $h$; $PE = U_s$ $mgh = \frac{1}{2}k(\Delta x)^2$ $h = \frac{k~(\Delta x)^2}{2mg}$ (b) We can use the expression from part (a) to find the maximum height $h$; $h = \frac{k~(\Delta x)^2}{2mg}$ $h = \frac{(25~N/m)(0.10~m)^2}{(2)(0.050~kg)(9.80~m/s^2)}$ $h = 0.26~m$ The ice cube goes up to a height of 0.26 m.