FrictionEdexcel A-Level Maths: Subtopic test

1. 1
   A box of mass 10 kg rests on a rough horizontal floor. The coefficient of friction between the box and the floor is 0.3. A horizontal force is applied to the box. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   The applied force is 25 N and the box remains at rest. Find the magnitude of the friction force on the box.

   [1 mark]

   • A$29.4$ N
   • B$25$ N
   • C$4.4$ N
   • D$0$ N

   (b)

   The applied force is increased to 35 N. Find the acceleration of the box.

   [1 mark]

   • A$0.56\ \text{m s}^{-2}$
   • B$3.5\ \text{m s}^{-2}$
   • C$6.44\ \text{m s}^{-2}$
   • D$5.6\ \text{m s}^{-2}$

   (c)

   Explain why the friction force in part (a) is 25 N and not $\mu R$, and state the greatest horizontal force that can be applied without the box moving.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A particle of mass 5 kg is placed on a rough plane inclined at $20^\circ$ to the horizontal. The coefficient of friction between the particle and the plane is $\mu$. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   The particle is in equilibrium. Find the magnitude of the friction force.

   [1 mark]

   • A$46.0$ N
   • B$49.0$ N
   • C$17.8$ N
   • D$16.8$ N

   (b)

   The particle is in equilibrium. Which condition on $\mu$ must be satisfied?

   [1 mark]

   • A$\mu\ge0.342$
   • B$\mu\le0.364$
   • C$\mu\ge0.364$
   • D$\mu\ge0.940$

   (c)

   The coefficient of friction is now 0.3 and the particle slides down the plane. Find its acceleration.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A crate of mass 20 kg is pulled along a rough horizontal floor by a light rope inclined at $30^\circ$ above the horizontal. The tension in the rope is 80 N, the crate is moving and the coefficient of friction between the crate and the floor is 0.25. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the magnitude of the normal reaction of the floor on the crate and the magnitude of the friction force.

   [3 marks]

   (b)

   Find the acceleration of the crate, and the speed of the crate after it has moved 5 m from rest.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A block $B$ of mass 6 kg lies on a rough horizontal table. The coefficient of friction between $B$ and the table is 0.4. $B$ is attached to a particle $C$ of mass 4 kg by a light inextensible string that passes over a smooth pulley at the edge of the table, with $C$ hanging freely. The system is released from rest with the string taut. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the acceleration of the particles and the tension in the string.

   [6 marks]

   (b)

   $C$ is initially 1.2 m above the floor and does not rebound on landing. $B$ is a long way from the pulley. Find the total distance moved by $B$ from release until it comes to rest.

   [6 marks]

   Total for question 4: 12 marks

End of questions