A 2 kg block is pressed against a rough vertical wall by a perpendicular force of 40 N . The coefficient of static friction is 0.5 . A second horizontal force of 15 N is applied to the block, acting parallel to the wall. Determine if the block will move. If it moves, find its direction relative to the 15 N force; if it does not move, find the magnitude of the frictional force exerted by the wall. (Take g = 10 m/s ^2

Step-by-step solution

Normal force exerted by the wall on the block is N = 40 N . Maximum static frictional force is f_ max = _s N = 0.5 40 = 20 N . The forces acting on the block parallel to the wall are its weight W = mg = 2 10 = 20 N acting vertically downwards and the applied horizontal force F = 15 N . The net driving force on the block is F_ net = F^2 + W^2 = 15^2 + 20^2 = 225 + 400 = 25 N . Since F_ net > f_ max , the block will move. The direction of motion will be along the net driving force. Let be the angle it makes with the