A block of mass m is on a horizontal surface with which its coefficient of kinetic friction is µk. The block is pushed against the free end of a light spring with force constant k, compressing the spring by distance d. Then the block is released from rest so that the spring fires the block across the surface. Of the possible expressions (a) through (k) listed below for the speed of the block after it has slid over distance d, (i) which cannot be true because they are dimensionally incorrect? (ii) Of those remaining, which give(s) an incorrect result in the limit as k becomes very large? (iii) Of those remaining, which give(s) an incorrect result in the limit as µk goes to zero? (iv) Of those remaining, which can you rule out for other reasons you specify? (v) Which expression is correct? (iv) Evaluate the speed in the case m = 250 g, µk = 0.600, k = 18.0 N/m, and d = 12.0 cm. You will need to explain your answer. (a) (kd2 ‒ µkmgd)1/2 (b) (kd2/m ‒ µkg)1/2 (c) (kd/m ‒ 2µkgd)1/2 (d) (kd2/m ‒ gd)1/2 (e) (f) kd2/m ‒ µkgd (g) (µkkd2/m ‒ gd)1/2 (h) (kd2/m ‒ 2µkgd)1/2 (i) (µkgd ‒ kd2/m)1/2 (j) (gd ‒ µkgd)1/2 (k) (kd2/m ‒ µkgd)1/2
