Year: 2003
Paper: 2
Question Number: 10
Course: LFM Pure and Mechanics
Section: Friction
No solution available for this problem.
Difficulty Rating: 1600.0
Difficulty Comparisons: 0
Banger Rating: 1500.0
Banger Comparisons: 0
A bead $B$ of mass $m$ can slide along a rough horizontal wire.
A light inextensible string of length $2\ell$ has one end attached
to a fixed point $A$
of the wire and the other to $B\,$.
A particle $P$ of mass $3m$ is attached to the mid-point of the string
and $B$ is held at a distance
$\ell$ from~$A\,$. The bead is released from rest.
Let $a_1$ and $a_2$ be the magnitudes of the horizontal and vertical components of the
initial acceleration of $P\,$. Show by considering the motion of $P$ relative to $A\,$, or
otherwise, that $a_1= \sqrt 3 a_2\,$. Show also that the magnitude
of the initial acceleration of $B$ is
$2a_1\,$.
Given that the frictional force opposing the motion
of $B$ is equal to $({\sqrt{3}}/6)R$, where $R$ is the normal reaction
between $B$ and the wire, show that the magnitude of the initial acceleration of
$P$ is~$g/18\,$.