Block A of mass 5.0 kg and block X are attached to a rope which passes over a pulley,as shown in the figure.An 80-N force P is applied horizontally to block A,keeping it in contact with a rough vertical face.The coefficients of static and kinetic friction between the wall and block A are μ_s = 0.40 and μ_k = 0.30.The pulley is light and frictionless.The mass of block X is adjusted until block A moves upward with an acceleration of 1.6 m/s².What is the mass of block X? A) 9.9 kg B) 9.3 kg C) 8.7 kg D) 8.1 kg E) 7.5 kg

Question

Quizplus · Accepted Answer

First, we need to calculate the force of friction acting on block A. Since it is in contact with the rough vertical face, the frictional force will be equal to μ_s times the normal force. The normal force will be equal to the weight of block A, which is 5.0 kg times 9.8 m/s² or 49 N. Therefore, the frictional force is 0.40 times 49 N or 19.6 N. Next, we need to calculate the net force acting on block A. Since it is being pulled to the right with an 80-N force and the friction is acting to the left with a force of 19.6 N, the net force is (80 N - 19.6 N) or 60.4 N. The tension in the rope is the same on both sides of the pulley, so the force pulling block X upward is also 60.4 N. We can use this information to calculate the mass of block X: F = ma 60.4 N = (5.0 kg + m) × 1.6 m/s² m = 9.9 kg

Block a of Mass 5