NYJC_EJC 2026 Forces Tutorial

9814 H3 Physics (2026) 1 Forces 1 A Level S Paper N00 Q2 The figure shows a smooth, hemispherical bowl of radius r, fixed to a horizontal table. A friend gives you a uniform, smooth rod of length L and weight W, and challenges you to find an angle  (the angle the rod makes with horizontal) such that the rod will rest in equilibrium on the rounded rim of the bowl. (a) Draw a labelled diagram showing the three forces acting on the rod when it is in equilibrium. Make clear the directions and lines of action of these forces. [3] (b) By resolving these forces vertically and horizontally and by taking moments about the lower end of the rod, show that the condition for equilibrium is =4 cos2 cosrL [5] [Hint: − = +cos( ) cos cos sin sinA B A B A B ] 2 A block of mass M sits on a plane that is inclined at an angle  to the horizontal as shown in Fig 1.1. Fig 2.1 (a) Assume that the frictional force between the block and plane is large enough to keep the block at rest and the coefficient of static friction is µ. (i) Determine the horizontal components of the normal and friction forces acting on the block. (ii) Determine the angle  at which these horizontal components are a maximum. L r 

9814 H3 Physics (2026) 2 (b) A horizontal force F = Mg is applied on the block, as shown in Fig 1.2. Assume that the frictional force between the block and plane is large enough to keep the block at rest and the coefficient of static friction is µ. Fig 1.2 (i) Determine the normal and friction forces acting on the block. (ii) Show that the range of  for which the block will remain at rest is given by:   −+ +− 11 tan11 . 3 A Level S Paper N02 Q7 (a) A smooth wire XYZ is bent to form a right angle at Y and is fixed in a vertical plane, as shown in Fig. 3.1. XY makes an angle of 30° to the horizontal. Fig. 3.1 Rings A and B, of mass m1 and m2 respectively, are placed on the wire and are connected by a light thread. The rings move without friction on the wire. When the system is in equilibrium, the thread makes an angle  with XY, as shown. (i) Ring A is in equilibrium under the action of three forces. List these forces, stating the direction of each. Sketch a vector triangle of the three forces. Label the sides and angle of the triangle. Explain why it is not possible to obtain the value of  from this triangle; [5] (ii) Ring B is also in equilibrium under the action of three forces. Sketch a labeled vector triangle of these forces. [2] (iii) Use your answers in (i) and (ii) to find an expression for  in terms of m1 and m2.