A block of mass 4 kg is pulled up along a rough inclined plane of angle 30^ with the horizontal by a force of 70 N acting parallel to the plane. If the coefficient of kinetic friction between the block and the plane is 3 2 , what is the acceleration of the block? (Take g = 10 m s ⁻² )

Step-by-step solution

Forces acting on the block along the inclined plane are: 1. Applied force F = 70 N (upwards) 2. Component of weight mg 30^ (downwards) 3. Kinetic friction f_k = _k N = _k mg 30^ (downwards) Calculating the downward forces: mg 30^ = 4 10 0.5 = 20 N f_k = 3 2 4 10 3 2 = 30 N Net force acting up the plane: F_ net = F - (mg 30^ + f_k) F_ net = 70 - (20 + 30) = 20 N Using Newton's second law: a = F_ net m = 20 4 = 5 m s ⁻² Answer: 5 m s ⁻²