Name: _______________________________________________
Edexcel AS Level Further Mathematics : Further Mechanics
Momentum and impulse
Date:
Time:
Total marks available:
Total marks achieved: ______
Questions
,Q1.
A small ball of mass 0.3 kg is released from rest from a point 3.6 m above horizontal ground. The
ball falls freely under gravity, hits the ground and rebounds vertically upwards.
In the first impact with the ground, the ball receives an impulse of magnitude 4.2 N s. The ball is
modelled as a particle.
(a) Find the speed of the ball immediately after it first hits the ground.
(5)
(b) Find the kinetic energy lost by the ball as a result of the impact with the ground.
(3)
(Total for question = 8 marks)
Q2.
Unless otherwise indicated, whenever a numerical value of g is required, take g = 9.8 m s–2 and
give your answer to either 2 significant figures or 3 significant figures.
A particle P of mass 3m is moving in a straight line on a smooth horizontal table.
A particle Q of mass m is moving in the opposite direction to P along the same straight line. The
particles collide directly. Immediately before the collision the speed of P is u and the speed of Q
is 2u. The velocities of P and Q immediately after the collision, measured in the direction of
motion of P before the collision, are v and w respectively. The coefficient of restitution between P
and Q is e.
(a) Find an expression for v in terms of u and e.
(6)
Given that the direction of motion of P is changed by the collision,
(b) find the range of possible values of e.
(2)
(c) Show that w = (1 + 9e).
(2)
Following the collision with P, the particle Q then collides with and rebounds from a fixed vertical
wall which is perpendicular to the direction of motion of Q. The coefficient of restitution between
Q and the wall is f.
, Given that e =
, and that P and Q collide again in the subsequent motion,
(d) find the range of possible values of f.
(6)
(Total for question = 16 marks)
Q3.
A particle P of mass 2m kg is moving with speed 2u m s–1 on a smooth horizontal plane. Particle
P collides with a particle Q of mass 3m kg which is at rest on the plane. The coefficient of
restitution between P and Q is e. Immediately after the collision the speed of Q is v m s–1
(a) Show that
(6)
(b) Show that
(2)
Given that the direction of motion of P is reversed by the collision,
(c) find, in terms of u and e, the speed of P immediately after the collision.
(2)
After the collision, Q hits a wall, that is fixed at right angles to the direction of motion of Q, and
rebounds.
The coefficient of restitution between Q and the wall is
Given that P and Q collide again,
(d) find the full range of possible values of e.
(5)
(Total for question = 15 marks)
Edexcel AS Level Further Mathematics : Further Mechanics
Momentum and impulse
Date:
Time:
Total marks available:
Total marks achieved: ______
Questions
,Q1.
A small ball of mass 0.3 kg is released from rest from a point 3.6 m above horizontal ground. The
ball falls freely under gravity, hits the ground and rebounds vertically upwards.
In the first impact with the ground, the ball receives an impulse of magnitude 4.2 N s. The ball is
modelled as a particle.
(a) Find the speed of the ball immediately after it first hits the ground.
(5)
(b) Find the kinetic energy lost by the ball as a result of the impact with the ground.
(3)
(Total for question = 8 marks)
Q2.
Unless otherwise indicated, whenever a numerical value of g is required, take g = 9.8 m s–2 and
give your answer to either 2 significant figures or 3 significant figures.
A particle P of mass 3m is moving in a straight line on a smooth horizontal table.
A particle Q of mass m is moving in the opposite direction to P along the same straight line. The
particles collide directly. Immediately before the collision the speed of P is u and the speed of Q
is 2u. The velocities of P and Q immediately after the collision, measured in the direction of
motion of P before the collision, are v and w respectively. The coefficient of restitution between P
and Q is e.
(a) Find an expression for v in terms of u and e.
(6)
Given that the direction of motion of P is changed by the collision,
(b) find the range of possible values of e.
(2)
(c) Show that w = (1 + 9e).
(2)
Following the collision with P, the particle Q then collides with and rebounds from a fixed vertical
wall which is perpendicular to the direction of motion of Q. The coefficient of restitution between
Q and the wall is f.
, Given that e =
, and that P and Q collide again in the subsequent motion,
(d) find the range of possible values of f.
(6)
(Total for question = 16 marks)
Q3.
A particle P of mass 2m kg is moving with speed 2u m s–1 on a smooth horizontal plane. Particle
P collides with a particle Q of mass 3m kg which is at rest on the plane. The coefficient of
restitution between P and Q is e. Immediately after the collision the speed of Q is v m s–1
(a) Show that
(6)
(b) Show that
(2)
Given that the direction of motion of P is reversed by the collision,
(c) find, in terms of u and e, the speed of P immediately after the collision.
(2)
After the collision, Q hits a wall, that is fixed at right angles to the direction of motion of Q, and
rebounds.
The coefficient of restitution between Q and the wall is
Given that P and Q collide again,
(d) find the full range of possible values of e.
(5)
(Total for question = 15 marks)
