9709 P43 - Jun 2017 - Q7
Two particles A and B of masses m kg and 4 kg respectively are connected by a light inextensible string that passes over a fixed smooth pulley. Particle A is on a rough fixed slope which is at an angle of 30° to the horizontal ground. Particle B hangs vertically below the pulley and is 0.5 m above the ground (see diagram). The coefficient of friction between the slope and particle A is 0.2.
(i) In the case where the system is in equilibrium with particle A on the point of moving directly up the slope, show that m = 5.94, correct to 3 significant figures.
(ii) In the case where m = 3, the system is released from rest with the string taut. Find the total distance travelled by A before coming to instantaneous rest. You may assume that A does not reach the pulley.
