The block of mass 'm' initially at x = 0 is acted upon by a horizontal force F = a - bx as shown in the figure. The coefficient of friction between the surfaces of contact is μ . The net work done on the block is zero if the block travels a distance of ________.

Step-by-step solution

f = a - bx f n ef = a - bx - f s For block to move at x = 0 a - b x > f s max = μ mg a > μ mg , So we are assuming motion starts at x = 0 w = ∫ a - bx - μ mg dx o = ax - bx 2 2 - μ mgx ⇒ x a - bx 2 - μ mg = 0 x = 0 a - bx 2 - μ mg = 0 bx 2 = a - μ mg x = 2 b a - μ mg