Momentum and impulse in one dimensionEdexcel A-Level Further Maths: Subtopic test

1. 1
   A cricket ball of mass $0.4$ kg is moving horizontally at $6$ m s$^{-1}$ towards a batsman. It is hit straight back along the same line and leaves the bat with speed $9$ m s$^{-1}$. The ball is in contact with the bat for $0.015$ s.

   (a)

   Find the magnitude of the impulse the bat exerts on the ball.

   [1 mark]

   • A$1.2$ N s
   • B$3.6$ N s
   • C$6.0$ N s
   • D$2.4$ N s

   (b)

   Find the magnitude of the average force exerted by the bat on the ball.

   [1 mark]

   • A$400$ N
   • B$80$ N
   • C$0.09$ N
   • D$240$ N

   (c)

   The same impulse is given to a ball of mass $0.4$ kg that is initially at rest. Find the speed it acquires.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Particle $A$, of mass $3$ kg, moves at $6$ m s$^{-1}$ along a smooth horizontal surface and collides directly with particle $B$, of mass $5$ kg, which is at rest. After the collision $A$ moves with speed $1$ m s$^{-1}$ in the opposite direction to its original motion. The collision lasts $0.03$ s.

   (a)

   Find the speed of $B$ immediately after the collision.

   [1 mark]

   • A$3.0$ m s$^{-1}$
   • B$3.6$ m s$^{-1}$
   • C$2.25$ m s$^{-1}$
   • D$4.2$ m s$^{-1}$

   (b)

   Find the magnitude of the impulse exerted on $A$ by $B$.

   [1 mark]

   • A$15$ N s
   • B$21$ N s
   • C$18$ N s
   • D$12.6$ N s

   (c)

   Find the magnitude and direction of the average force exerted by $A$ on $B$ during the collision.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Particle $P$, of mass $2$ kg, moves at $6$ m s$^{-1}$ and particle $Q$, of mass $3$ kg, moves at $2$ m s$^{-1}$ in the opposite direction, along the same straight line on a smooth horizontal surface. They collide directly and coalesce to form a single particle $R$.

   (a)

   Find the speed and direction of $R$ immediately after the collision.

   [3 marks]

   (b)

   Find the magnitude of the impulse that $P$ exerts on $Q$, and the magnitude of the average force between them if the collision lasts $0.04$ s.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Three particles $A$, $B$ and $C$ have masses $2$ kg, $3$ kg and $5$ kg. They lie on a straight line on a smooth horizontal surface, with $C$ at rest. $A$ and $B$ move towards each other, $A$ at $6$ m s$^{-1}$ and $B$ at $2$ m s$^{-1}$, and collide directly. After this collision $A$ moves with speed $3$ m s$^{-1}$ in the opposite direction to its original motion, and $B$ then moves towards $C$.

   (a)

   (i) Find the speed of $B$ immediately after the collision with $A$, and state its direction.
   (ii) Find the magnitude and direction of the impulse exerted on $A$ by $B$.

   [6 marks]

   (b)

   $B$ now collides directly with $C$ and the two particles coalesce. The combined particle then hits a fixed buffer and is brought to rest in $0.25$ s. Find the magnitude of the average force exerted by the buffer.

   [6 marks]

   Total for question 4: 12 marks

End of questions