1999 Paper 3 Q10

Year: 1999
Paper: 3
Question Number: 10

Course: UFM Mechanics
Section: Momentum and Collisions 1

Difficulty: 1700.0 Banger: 1484.0

momentum impulse inelastic collision chain problem summation to integral approximation falling chain variable mass

Problem

A chain of mass \(m\) and length \(l\) is composed of \(n\) small smooth links. It is suspended vertically over a horizontal table with its end just touching the table, and released so that it collapses inelastically onto the table. Calculate the change in momentum of the \((k+1)\)th link from the bottom of the chain as it falls onto the table. Write down an expression for the total impulse sustained by the table in this way from the whole chain. By approximating the sum by an integral, show that this total impulse is approximately \[ {\textstyle \frac23} m \surd(2gl) \] when \(n\) is large.

No solution available for this problem.

Rating Information

Difficulty Rating: 1700.0

Difficulty Comparisons: 0

Banger Rating: 1484.0

Banger Comparisons: 1

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Problem source

A chain of mass $m$ and length $l$ is composed of $n$ small smooth  links.
It is suspended vertically over a horizontal table with
its end just touching the table, and released so that it
collapses inelastically onto the table.
Calculate the change in momentum of the $(k+1)$th link from the bottom
of the chain as it
falls onto the table.
Write down an expression for the total impulse sustained by the table 
in this way from  the whole chain. By approximating the
sum by an integral, show that 
this  
total impulse  is approximately 
\[
{\textstyle \frac23} m \surd(2gl)
\]
when $n$ is large.

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