Newton's third law and connected particlesEdexcel A-Level Maths: Subtopic test

1. 1
   A lift of mass 250 kg carries a person of mass 70 kg. The lift is raised by a vertical cable and accelerates upwards at $1.5\ \text{m s}^{-2}$. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the magnitude of the normal reaction of the floor of the lift on the person.

   [1 mark]

   • A$581$ N
   • B$686$ N
   • C$791$ N
   • D$105$ N

   (b)

   Which statement describes the force that the person exerts on the floor of the lift?

   [1 mark]

   • A$791$ N acting downwards on the floor
   • B$791$ N acting upwards on the person
   • C$686$ N acting downwards on the floor
   • D$581$ N acting downwards on the floor

   (c)

   Find the tension in the cable.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Particle $A$ of mass 3 kg and particle $B$ of mass 5 kg are attached to the ends of a light inextensible string that passes over a smooth fixed pulley. The particles hang vertically and are released from rest with the string taut. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the acceleration of the particles.

   [1 mark]

   • A$1.96\ \text{m s}^{-2}$
   • B$1.225\ \text{m s}^{-2}$
   • C$4.9\ \text{m s}^{-2}$
   • D$2.45\ \text{m s}^{-2}$

   (b)

   Find the tension in the string.

   [1 mark]

   • A$29.4$ N
   • B$49$ N
   • C$7.35$ N
   • D$36.75$ N

   (c)

   Particle $B$ is initially 1.5 m above the floor. Find the speed with which $B$ hits the floor.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two blocks, $P$ of mass 4 kg and $Q$ of mass 6 kg, are in contact on a horizontal surface. A horizontal force of magnitude 30 N is applied to $P$, directed towards $Q$, and the blocks move together in a straight line.

   (a)

   The surface is smooth. Find the acceleration of the blocks and the magnitude of the contact force between them.

   [3 marks]

   (b)

   The surface is rough. The resistance to motion is 5 N on $P$ and 7 N on $Q$. Find the acceleration of the blocks and the magnitude of the contact force between them.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Particle $A$ of mass 2 kg lies on a smooth horizontal table. It is attached to particle $B$ of mass 3 kg by a light inextensible string that passes over a smooth pulley fixed at the edge of the table, with $B$ hanging freely. The system is released from rest with the string taut and $A$ at distance 1.5 m from the pulley. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the acceleration of the particles and the tension in the string, and state what each of the modelling assumptions "light string" and "inextensible string" allows you to assume.

   [6 marks]

   (b)

   $B$ is 0.9 m above the floor when released and does not rebound on landing. Assuming the table is long enough and $A$ does not reach the pulley before $B$ lands, find the total time from release until $A$ reaches the pulley.

   [6 marks]

   Total for question 4: 12 marks

End of questions