Connected particles, pulleys and inclined planesEdexcel International A Level Maths: Mind map

Exam questions on Connected particles, pulleys and inclined planes

1. Two particles $A$ and $B$, of masses $3$ kg and $5$ kg, are attached to the ends of a light inextensible string. The string passes over a smooth fixed pulley and the particles hang vertically with the string taut. The system is released from rest. Take $g=9.8$ m s⁻².
   Find the magnitude of the force exerted on the pulley by the string.2 marks
2. Particles $P$ and $Q$, of masses $3$ kg and $2$ kg, are attached to the ends of a light inextensible string that passes over a smooth fixed pulley. Initially $Q$ is on horizontal ground and $P$ is $1.2$ m above the ground, with the string taut and vertical. The system is released from rest. After $P$ hits the ground it does not rebound. In the motion described, $Q$ does not reach the pulley. Take $g=9.8$ m s⁻².
   After $P$ hits the ground, find the further distance that $Q$ rises before it first comes to rest.2 marks
3. A particle of mass $4$ kg is on a smooth plane inclined at $30^\circ$ to the horizontal. Take $g=9.8$ m s⁻².
   The particle is released from rest. Find its acceleration down the plane.3 marks