1993 Paper 3 Q12

Year: 1993
Paper: 3
Question Number: 12

Course: UFM Mechanics
Section: Work, energy and Power 2

Difficulty: 1700.0 Banger: 1432.3

elastic string energy conservation Hooke's law equilibrium modulus of elasticity quadratic equation tension pegs work-energy theorem

Problem

\(ABCD\) is a horizontal line with \(AB=CD=a\) and \(BC=6a\). There are fixed smooth pegs at \(B\) and \(C\). A uniform string of natural length \(2a\) and modulus of elasticity \(kmg\) is stretched from \(A\) to \(D\), passing over the pegs at \(B\) and \(C\). A particle of mass \(m\) is attached to the midpoint \(P\) of the string. When the system is in equilibrium, \(P\) is a distance \(a/4\) below \(BC\). Evaluate \(k\). The particle is pulled down to a point \(Q\), which is at a distance \(pa\) below the mid-point of \(BC\), and is released from rest. \(P\) rises to a point \(R\), which is at a distance \(3a\) above \(BC\). Show that \(2p^2-p-17=0\). Show also that the tension in the strings is less when the particle is at \(R\) than when the particle is at \(Q\).

No solution available for this problem.

Rating Information

Difficulty Rating: 1700.0

Difficulty Comparisons: 0

Banger Rating: 1432.3

Banger Comparisons: 5

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Problem source

$ABCD$ is a horizontal line with 
$AB=CD=a$ and $BC=6a$. 
There are
fixed smooth pegs at $B$ and $C$.
A uniform string of natural length $2a$ and modulus of elasticity
$kmg$ is stretched from $A$ to $D$, passing over the pegs at 
$B$ and $C$. A particle of mass $m$ is attached to the midpoint $P$
of the string.  When the
system is in equilibrium, $P$ is a distance $a/4$ below $BC$. Evaluate
$k$.
The particle is pulled down to a point $Q$, which is
at a distance $pa$ below
the mid-point of $BC$, and is released from rest. $P$ rises to 
a point $R$, which is at 
 a distance $3a$ above $BC$. Show that $2p^2-p-17=0$.
Show also that the tension in the strings is less when the 
particle is at $R$ than when the particle is at $Q$.

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