NJC 02P. Forces and Moments

National Junior College Science Department | Physics 1 02 Forces and Moments PROBLEM SET These problems are for both H1 Physics and H2 Physics. Duration: 2.5 hours 1 Fig. 1.1 shows a force diagram that represents a boat that is being lifted by two ropes so that the boat remains horizontal and travels vertically upwards at a constant speed after leaving the water. Fig. 1.1 The weight of the boat is 15000 N and the tensions in the ropes 1 and 2 are T1 and T2 respectively. (a) The position of the centre of gravity of the boat is not at its midpoint. Suggest what this implies about the distribution of mass in the boat. [1] (b) Explain two conditions required for the boat to be in a state of equilibrium while it is moving upwards. [2] (c) Use the principle of moments to determine the tensions in the two ropes. [4] (2009 P2 Q3)

National Junior College Science Department | Physics 2 2 (a) State the principle of moments. [1] (b) A metal sign of uniform thickness and of width 1.00 m at its upper edge hangs from two vertical, rigid supports, as shown in Fig. 2.1. Fig. 2.1 The sign is hinged and swings freely from the rigid supports at points A and B. The supports are 0.20 m from each edge of the sign. The mass of the sign is 4.5 kg. The centre of mass of the sign is 0.32 m below its upper edge. (i) The ratio of the tensions in the two supports is 3 7. Calculate the magnitude of each tension. [2] (ii) Using your answers to (b)(i), determine the horizontal distance d of the centre of mass from the left edge of the metal sign. [2] (c) A horizontal wind now blows on the face of the sign so it hangs at an angle 𝜃 to the vertical, as shown in Fig. 2.2.

National Junior College Science Department | Physics 3 Fig. 2.2 Explain why the force exerted by each support on the sign now has a horizontal component. [1] (2018 P2 Q1) 3 A non-uniform bar AB makes an angle of 60° with a horizontal surface, as shown in Fig. 3.1. Fig. 3.1 The bar is hinged at A and is supported by a rod at B. The force X produced by the rod at B acts at an angle of 70° to the horizontal. The bar has a length of 1.2 m and a weight of 36 N. The centre of gravity of the bar is 0.45 m from A. (a) Use the principle of moments to show that the magnitude of X is 8.8 N. [2] (b) A force F acts on the bar at A. (i) Explain why a force is required to act on the bar at A to keep the bar in equilibrium.

National Junior College Science Department | Physics 4 [2] (ii) Calculate the magnitude of F. [3] (iii) On Fig. 3.1, draw an arrow to show the approximate direction of F. [1] (2016 P2 Q3) 4 A sign PQ and its support stand are in equilibrium on a horizontal surface, as shown in Fig. 4.1. Fig. 4.1 (not to scale) The sign is uniform and has a mass of 2.3 kg. The sign is at an angle of 58° to the