College Physics (4th Edition)

(a) A minimum force of 15.78 N is required to make the block start to slide. (b) Since the net force is non-zero, the block accelerates. (c) $a = 1.27~m/s^2$
(a) In order to make the block start moving, the minimum force $F$ required is equal in magnitude to the maximum possible value of the static friction force: $F = mg~\mu_s$ $F = (4.6~kg)(9.80~m/s^2)(0.35)$ $F = 15.78~N$ A minimum force of 15.78 N is required to make the block start to slide. (b) We can calculate the net force when the block is sliding: $\sum F = F-mg~\mu_k$ $\sum F = 15.78~N-(4.6~kg)(9.80~m/s^2)(0.22)$ $\sum F = 5.86~N$ Since the net force is non-zero, the block accelerates. (c) We can find the acceleration: $ma = \sum F$ $a = \frac{\sum F}{m}$ $a = \frac{5.86~N}{4.6~kg}$ $a = 1.27~m/s^2$