Name: _______________________________________________
Edexcel A Level Further Mathematics : Further Mechanics
Momentum and impulse
Date:
Time:
Total marks available:
Total marks achieved: ______
Questions
,Q1.
A particle P of mass 3m and a particle Q of mass 2m are moving along the same straight
line on a smooth horizontal plane. The particles are moving in opposite directions
towards each other and collide directly.
Immediately before the collision the speed of P is u and the speed of Q is 2u.
Immediately after the collision P and Q are moving in opposite directions.
The coefficient of restitution between P and Q is e.
(a) Find the range of possible values of e, justifying your answer.
(8)
Given that Q loses 75% of its kinetic energy as a result of the collision,
(b) find the value of e.
(3)
(Total for question = 11 marks)
Q2.
[In this question i and j are perpendicular unit vectors in a horizontal plane.]
A smooth uniform sphere A has mass 0.2 kg and another smooth uniform sphere B, with
the same radius as A, has mass 0.4 kg.
The spheres are moving on a smooth horizontal surface when they collide obliquely.
Immediately before the collision, the velocity of A is (3i + 2j) m s–1 and the velocity of B
is (–4i – j) m s–1
At the instant of collision, the line joining the centres of the spheres is parallel to i
The coefficient of restitution between the spheres is
(a) Find the velocity of A immediately after the collision.
(7)
(b) Find the magnitude of the impulse received by A in the collision.
(2)
, (c) Find, to the nearest degree, the size of the angle through which the direction of
motion of A is deflected as a result of the collision.
(3)
(Total for question = 12 marks)
Q3.
Unless otherwise indicated, whenever a numerical value of g is required, take g = 9.8 ms–2 and
give your answer to either 2 significant figures or 3 significant figures.
A particle P of mass 0.5 kg is moving with velocity (4i + j) m s–1 when it receives an impulse (2i –
j) N s.
Show that the kinetic energy gained by P as a result of the impulse is 12 J.
(6)
(Total for question = 6 marks)
Q4.
Unless otherwise indicated, whenever a numerical value of g is required, take g = 9.8 ms–2 and
give your answer to either 2 significant figures or 3 significant figures.
A particle of mass m kg lies on a smooth horizontal surface.
Initially the particle is at rest at a point O between two fixed parallel vertical walls.
The point O is equidistant from the two walls and the walls are 4 m apart.
At time t = 0 the particle is projected from O with speed u m s–1 in a direction perpendicular to
the walls.
The coefficient of restitution between the particle and each wall is
Edexcel A Level Further Mathematics : Further Mechanics
Momentum and impulse
Date:
Time:
Total marks available:
Total marks achieved: ______
Questions
,Q1.
A particle P of mass 3m and a particle Q of mass 2m are moving along the same straight
line on a smooth horizontal plane. The particles are moving in opposite directions
towards each other and collide directly.
Immediately before the collision the speed of P is u and the speed of Q is 2u.
Immediately after the collision P and Q are moving in opposite directions.
The coefficient of restitution between P and Q is e.
(a) Find the range of possible values of e, justifying your answer.
(8)
Given that Q loses 75% of its kinetic energy as a result of the collision,
(b) find the value of e.
(3)
(Total for question = 11 marks)
Q2.
[In this question i and j are perpendicular unit vectors in a horizontal plane.]
A smooth uniform sphere A has mass 0.2 kg and another smooth uniform sphere B, with
the same radius as A, has mass 0.4 kg.
The spheres are moving on a smooth horizontal surface when they collide obliquely.
Immediately before the collision, the velocity of A is (3i + 2j) m s–1 and the velocity of B
is (–4i – j) m s–1
At the instant of collision, the line joining the centres of the spheres is parallel to i
The coefficient of restitution between the spheres is
(a) Find the velocity of A immediately after the collision.
(7)
(b) Find the magnitude of the impulse received by A in the collision.
(2)
, (c) Find, to the nearest degree, the size of the angle through which the direction of
motion of A is deflected as a result of the collision.
(3)
(Total for question = 12 marks)
Q3.
Unless otherwise indicated, whenever a numerical value of g is required, take g = 9.8 ms–2 and
give your answer to either 2 significant figures or 3 significant figures.
A particle P of mass 0.5 kg is moving with velocity (4i + j) m s–1 when it receives an impulse (2i –
j) N s.
Show that the kinetic energy gained by P as a result of the impulse is 12 J.
(6)
(Total for question = 6 marks)
Q4.
Unless otherwise indicated, whenever a numerical value of g is required, take g = 9.8 ms–2 and
give your answer to either 2 significant figures or 3 significant figures.
A particle of mass m kg lies on a smooth horizontal surface.
Initially the particle is at rest at a point O between two fixed parallel vertical walls.
The point O is equidistant from the two walls and the walls are 4 m apart.
At time t = 0 the particle is projected from O with speed u m s–1 in a direction perpendicular to
the walls.
The coefficient of restitution between the particle and each wall is
