FrictionEdexcel International A Level Maths: Subtopic test

1. 1
   A box of mass $12$ kg rests on a rough horizontal floor. The coefficient of friction between the box and the floor is $0.35$. A horizontal force of magnitude $P$ N is applied to the box. Take $g=9.8$ m s⁻².

   (a)

   Find the maximum friction that the floor can exert on the box.

   [1 mark]

   • A$4.2$ N
   • B$41.2$ N
   • C$117.6$ N
   • D$76.4$ N

   (b)

   The force $P=30$. Find the magnitude of the friction force acting on the box.

   [1 mark]

   • A$41.2$ N
   • B$0$ N
   • C$30$ N
   • D$11.2$ N

   (c)

   The force $P$ is now increased to $50$. Find the acceleration of the box.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A block of mass $10$ kg rests on a rough plane inclined at an angle $\alpha$ to the horizontal, where $\tan\alpha=\frac34$. The block is on the point of sliding down the plane. Take $g=9.8$ m s⁻².

   (a)

   Find the normal reaction between the block and the plane.

   [1 mark]

   • A$58.8$ N
   • B$98$ N
   • C$122.5$ N
   • D$78.4$ N

   (b)

   Find the coefficient of friction between the block and the plane.

   [1 mark]

   • A$0.75$
   • B$0.6$
   • C$0.8$
   • D$1.33$

   (c)

   The block is replaced by one of mass $20$ kg of the same material. Without calculating friction forces, state whether the block will slide down the plane, giving a reason.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle $P$ of mass $2$ kg is on a rough horizontal floor. The coefficient of friction between $P$ and the floor is $0.4$. The particle is pulled by a light rope inclined at $25^\circ$ above the horizontal. The tension in the rope is $T$ N. Take $g=9.8$ m s⁻².

   (a)

   Find the least value of $T$ for which the particle is on the point of moving.

   [3 marks]

   (b)

   The tension is now $T=10$. Find the acceleration of the particle.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A rough plane is inclined at $30^\circ$ to the horizontal. A particle $P$ of mass $6$ kg is on the plane. The coefficient of friction between $P$ and the plane is $0.5$. Take $g=9.8$ m s⁻².

   (a)

   A force of magnitude $X$ N is applied to $P$ up a line of greatest slope and $P$ remains in equilibrium. Find the range of possible values of $X$.

   [6 marks]

   (b)

   The force $X$ is removed and $P$ is projected up a line of greatest slope with speed $5$ m s⁻¹. Find the distance $P$ travels up the plane before first coming to rest, and determine whether $P$ then remains at rest.

   [6 marks]

   Total for question 4: 12 marks

End of questions