Momentum and impulseEdexcel International A Level Maths: Subtopic test

1. 1
   A ball of mass $0.4$ kg hits a smooth vertical wall at right angles with speed $12$ m s⁻¹ and rebounds along the same line with speed $8$ m s⁻¹.

   (a)

   Find the magnitude of the impulse exerted by the wall on the ball.

   [1 mark]

   • A$1.6$ N s
   • B$4.8$ N s
   • C$3.2$ N s
   • D$8$ N s

   (b)

   The ball is in contact with the wall for $0.05$ s. Find the magnitude of the average force exerted by the wall on the ball.

   [1 mark]

   • A$0.4$ N
   • B$160$ N
   • C$96$ N
   • D$32$ N

   (c)

   On a second occasion the ball hits the wall at right angles with speed $12$ m s⁻¹ and the magnitude of the impulse exerted by the wall is $6$ N s. Find the speed with which the ball rebounds.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Particles $A$ and $B$, of masses $3$ kg and $2$ kg, move towards each other along a straight line on a smooth horizontal surface. $A$ has speed $5$ m s⁻¹ and $B$ has speed $4$ m s⁻¹. The particles collide directly. After the collision $A$ has speed $1$ m s⁻¹ and its direction of motion is reversed.

   (a)

   Taking the original direction of motion of $A$ as positive, find the total momentum of the particles before the collision.

   [1 mark]

   • A$23$ kg m s⁻¹
   • B$-7$ kg m s⁻¹
   • C$7$ kg m s⁻¹
   • D$1$ kg m s⁻¹

   (b)

   Find the velocity of $B$ after the collision.

   [1 mark]

   • A$5$ m s⁻¹ in the original direction of $A$
   • B$2$ m s⁻¹ in the original direction of $A$
   • C$5$ m s⁻¹ in the original direction of $B$
   • D$13$ m s⁻¹ in the original direction of $A$

   (c)

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

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Particle $P$, of mass $4$ kg, moves with speed $6$ m s⁻¹ on a smooth horizontal surface and collides directly with particle $Q$, of mass $8$ kg, which is moving in the opposite direction with speed $2$ m s⁻¹. After the collision $P$ and $Q$ coalesce and move as a single particle.

   (a)

   Find the speed of the combined particle after the collision and the direction in which it moves.

   [3 marks]

   (b)

   Find the magnitude and direction of the impulse exerted by $P$ on $Q$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Particle $A$, of mass $3$ kg, is moving with speed $8$ m s⁻¹ along a straight line on a smooth horizontal surface. It collides directly with particle $B$, of mass $m$ kg, which is moving in the same direction with speed $2$ m s⁻¹. After the collision $A$ moves with speed $4$ m s⁻¹ and $B$ moves with speed $7$ m s⁻¹, both in the original direction of motion.

   (a)

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

   [6 marks]

   (b)

   $B$ then hits a fixed smooth vertical barrier, which is perpendicular to the line of motion and $21$ m from the point where the first collision took place. $B$ rebounds with speed $5$ m s⁻¹. Find the magnitude of the impulse exerted by the barrier on $B$, and the time between $B$ hitting the barrier and the second collision with $A$.

   [6 marks]

   Total for question 4: 12 marks

End of questions