1992 Paper 2 Q13

Year: 1992
Paper: 2
Question Number: 13

Course: UFM Mechanics
Section: Momentum and Collisions 1

Difficulty: 1600.0 Banger: 1484.0
momentum collisions friction inextensible string coefficient of restitution energy conservation Newtons second law particle on table connected particles

Problem

Two particles \(P_{1}\) and \(P_{2}\), each of mass \(m\), are joined by a light smooth inextensible string of length \(\ell.\) \(P_{1}\) lies on a table top a distance \(d\) from the edge, and \(P_{2}\) hangs over the edge of the table and is suspended a distance \(b\) above the ground. The coefficient of friction between \(P_{1}\) and the table top is \(\mu,\) and \(\mu<1\). The system is released from rest. Show that \(P_{1}\) will fall off the edge of the table if and only if \[ \mu<\frac{b}{2d-b}. \] Suppose that \(\mu>b/(2d-b)\) , so that \(P_{1}\) comes to rest on the table, and that the coefficient of restitution between \(P_{2}\) and the floor is \(e\). Show that, if \(e>1/(2\mu),\) then \(P_{1}\) comes to rest before \(P_{2}\) bounces a second time.

No solution available for this problem.

Rating Information

Difficulty Rating: 1600.0

Difficulty Comparisons: 0

Banger Rating: 1484.0

Banger Comparisons: 1

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Problem source
Two particles $P_{1}$ and $P_{2}$, each of mass $m$, are joined
by a light smooth inextensible string of length $\ell.$ $P_{1}$
lies on a table top a distance $d$ from the edge, and $P_{2}$ hangs
over the edge of the table and is suspended a distance $b$ above
the ground. The coefficient of friction between $P_{1}$ and the table
top is $\mu,$ and $\mu<1$. The system is released from rest. Show
that $P_{1}$ will fall off the edge of the table if and only if 
\[
\mu<\frac{b}{2d-b}.
\]
Suppose that $\mu>b/(2d-b)$ , so that $P_{1}$ comes to rest on the
table, and that the coefficient of restitution between $P_{2}$ and
the floor is $e$. Show that, if $e>1/(2\mu),$ then $P_{1}$ comes
to rest before $P_{2}$ bounces a second time.
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