Neco 2023 Physics Question 4

A block of mass \(5.0\,\text{kg}\) rests on a rough inclined plane that makes an angle of \(30^{\circ}\) with the horizontal. The coefficient of static friction between the block and the plane is \(0.25\). A light inextensible string passes over a frictionless pulley at the top of the plane and is attached to a hanging mass \(M\). The system is initially in equilibrium. In addition, a horizontal force of \(20\,\text{N}\) can be applied to the block as shown in the diagram. Answer the following: a) Determine the minimum value of the hanging mass \(M\) required to start moving the block up the plane. b) If the hanging mass is \(M = 3.0\,\text{kg}\) and the horizontal force of \(20\,\text{N}\) is applied, calculate the acceleration of the block up the plane. c) Draw a free‑body diagram for the block, label all the forces, and write the net‑force equation used in part (b).