Connected particles, pulleys and inclined planesEdexcel International A Level Maths: Subtopic test

1. 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.

   (a)

   Find the acceleration of the particles.

   [1 mark]

   • A$2.45$ m s⁻²
   • B$4.9$ m s⁻²
   • C$0.25$ m s⁻²
   • D$19.6$ m s⁻²

   (b)

   Find the tension in the string.

   [1 mark]

   • A$29.4$ N
   • B$49$ N
   • C$36.75$ N
   • D$22.05$ N

   (c)

   Find the magnitude of the force exerted on the pulley by the string.

   [2 marks]

   Total for question 1: 4 marks

2. 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.

   (a)

   Find the acceleration of $P$ before it hits the ground.

   [1 mark]

   • A$4.9$ m s⁻²
   • B$1.96$ m s⁻²
   • C$5.88$ m s⁻²
   • D$3.92$ m s⁻²

   (b)

   Find the speed of $P$ just before it hits the ground.

   [1 mark]

   • A$2.35$ m s⁻¹
   • B$4.85$ m s⁻¹
   • C$4.70$ m s⁻¹
   • D$2.17$ m s⁻¹

   (c)

   After $P$ hits the ground, find the further distance that $Q$ rises before it first comes to rest.

   [2 marks]

   Total for question 2: 4 marks

3. 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.

   (a)

   The particle is released from rest. Find its acceleration down the plane.

   [3 marks]

   (b)

   The particle is projected from a point $O$ up a line of greatest slope with speed $8$ m s⁻¹. Find the total time that elapses before the particle returns to $O$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Particle $A$, of mass $2$ kg, is on a rough plane inclined at $30^\circ$ to the horizontal. Particle $B$, of mass $3$ kg, hangs vertically. They are connected by a light inextensible string that passes over a smooth pulley fixed at the top edge of the plane, with the string parallel to a line of greatest slope. The coefficient of friction between $A$ and the plane is $0.4$. $B$ is $1.2$ m above horizontal ground and the system is released from rest with the string taut, so that $A$ moves up the plane. $A$ does not reach the pulley. Take $g=9.8$ m s⁻².

   (a)

   Find the acceleration of $A$ while $B$ is falling.

   [6 marks]

   (b)

   $B$ hits the ground and does not rebound. Find the further distance that $A$ moves up the plane before it first comes to rest.

   [6 marks]

   Total for question 4: 12 marks

End of questions