2005 Paper 3 Q9

Year: 2005
Paper: 3
Question Number: 9

Course: UFM Mechanics
Section: Momentum and Collisions 1

Difficulty: 1700.0 Banger: 1484.0
momentum collisions coefficient of restitution Newton's law of restitution conservation of momentum wall rebound geometric series equal time intervals two-particle collision recurrence

Problem

Two particles, A and B, move without friction along a horizontal line which is perpendicular to a vertical wall. The coefficient of restitution between the two particles is \(e\) and the coefficient of restitution between particle B and the wall is also \(e\), where \( 0< e < 1\). The mass of particle~A is \(4em\) (with \(m > 0\)), and the mass of particle B is \((1-e)^2m\)\,. Initially, A is moving towards the wall with speed \((1-e)v\) (where \(v > 0\)) and B is moving away from the wall and towards A with speed \(2ev\). The two particles collide at a distance \(d\) from the wall. Find the speeds of A and B after the collision. When B strikes the wall, it rebounds along the same line. Show that a second collision will take place, at a distance \(de\) from the wall. Deduce that further collisions will take place. Find the distance from the wall at which the \(n\)th collision takes place, and show that the times between successive collisions are equal.

No solution available for this problem.

Rating Information

Difficulty Rating: 1700.0

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Banger Rating: 1484.0

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Problem source
Two particles, A and B, 
move without friction along a horizontal line which is 
perpendicular to a vertical wall. 
The coefficient of restitution between the two particles is $e$ 
and the coefficient of restitution between particle B 
and the wall is also $e$, where $ 0<  e < 1$. 
The mass of particle~A is $4em$ (with $m > 0$), 
and the mass of particle B is $(1-e)^2m$\,. 
 
Initially, A is moving towards the wall with speed $(1-e)v$ 
(where $v > 0$) and B is moving away from the wall and towards A 
with speed $2ev$. The two particles collide at a 
distance $d$ from the wall. Find the speeds of A and B after the collision. 
 
When B strikes the wall, it rebounds along the same line. 
Show that a second collision will take place, 
at a distance $de$ from the wall. 
 
Deduce that further collisions will take place. Find 
the distance from the wall at which the $n$th collision takes place,
and show that the times between successive collisions are equal.
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