FrictionAQA A-Level Maths: Subtopic test

1. 1
   A box of mass $10$ kg rests on rough horizontal ground. The coefficient of friction between the box and the ground is $0.4$. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the normal reaction of the ground on the box.

   [1 mark]

   • A$9.8$ N
   • B$10$ N
   • C$39.2$ N
   • D$98$ N

   (b)

   Find the maximum friction force that the ground can exert on the box.

   [1 mark]

   • A$98$ N
   • B$245$ N
   • C$39.2$ N
   • D$4$ N

   (c)

   A horizontal force of magnitude $30$ N is applied to the box. Find the magnitude of the friction force, justifying your answer.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A block of mass $5$ kg is placed at rest on a rough plane inclined at $20^\circ$ to the horizontal. The coefficient of friction between the block and the plane is $0.5$. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the normal reaction of the plane on the block.

   [1 mark]

   • A$16.8$ N
   • B$46.0$ N
   • C$49.0$ N
   • D$23.0$ N

   (b)

   Assuming the block stays at rest, find the friction force acting on it.

   [1 mark]

   • A$16.8$ N
   • B$46.0$ N
   • C$23.0$ N
   • D$49.0$ N

   (c)

   Show that the block does remain at rest.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A crate of mass $20$ kg is pulled from rest along rough horizontal ground by a horizontal rope with tension $90$ N. The coefficient of friction between the crate and the ground is $0.3$. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the acceleration of the crate.

   [3 marks]

   (b)

   When the crate is moving at $4\ \text{m s}^{-1}$ the rope breaks. Find the distance the crate then slides before coming to rest.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A box of mass $15$ kg rests on rough horizontal ground. The coefficient of friction between the box and the ground is $0.35$. A light rope attached to the box is pulled with tension $T$ N at $30^\circ$ above the horizontal. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the least value of $T$ for which the box begins to move.

   [6 marks]

   (b)

   The tension is increased to $70$ N and the box starts from rest. After $4$ s the rope breaks. Find the distance the box slides after the rope breaks before it comes to rest.

   [6 marks]

   Total for question 4: 12 marks

End of questions