Answers:
LEVEL: AS
MATHS – Mechanics
11. Connected particles; constant acceleration (12 minutes)
Two particles A and B, having masses 3m kg and 7m kg respectively, hang on a light inextensible
string over a fixed light smooth pulley P. Initially, both portions of the string PA and PB are vertical
and A and B are at rest (see diagram).
2
For this question, assume that (i) g = 10ms− ; (ii) A never reaches the ground; (iii) neither particle ever
reaches the pulley.
Hints: always draw a force diagram for this kind of question. Be careful that each particle is labeled only with
the forces that it is experiencing.
For a smooth pulley, the tension is the same throughout the string. Also, since the particles are connected,
they must have equal and opposite accelerations as long as the string is taut. Choose a convention for
positive/negative directions at the beginning and stick to it!
(a) A and B are released. Find their initial accelerations.
(2 marks)
Let up be positive and down be negative.
Initially, A rises and B falls. For each particle, F = ma
For A,
For B,
(1)
(2)
Subtract equation (2) from equation (1)
Copyright © Pearson Education Limited 2001
1
Answers:
LEVEL: AS
MATHS – Mechanics
(b) After falling 2 m, B hits the ground and does not rebound. Find:
(i) the maximum height reached by A above its position when B hits the ground;
(5 marks)
When B hits the ground, the string becomes slack.
First find speed of A when B hits the ground. As B has fallen 2 m, A must have risen 2 m.
u = 0, v = ?, s = 2 m, a = 4ms−2
When the string goes slack, A continues to travel upwards, starting at this velocity, but now it has a
downward acceleration of g = -10ms−2. To find how much further it rises before reaching its maximum
height, remember that at maximum height A is instantaneously at rest, i.e. v = 0.
u = 4ms−1, v = 0, a = –10ms−2, s = ?
So A rises an additional 0.8m after B hits the ground.
(ii) the time taken for A to come to rest once B hits the ground.
(3 marks)
Calculate the time for A to rise:
u = 4ms−1, v = 0, a = –10ms−2, t = ?
(Total marks 10)
Copyright © Pearson Education Limited 2001
2