Year: 2011
Paper: 3
Question Number: 10
Course: UFM Mechanics
Section: Work, energy and Power 2
No solution available for this problem.
The percentages attempting larger numbers of questions were higher this year than formerly. More than 90% attempted at least five questions and there were 30% that didn't attempt at least six questions. About 25% made substantive attempts at more than six questions, of which a very small number indeed were high scoring candidates that had perhaps done extra questions (well) for fun, but mostly these were cases of candidates not being able to complete six good solutions.
Difficulty Rating: 1700.0
Difficulty Comparisons: 0
Banger Rating: 1486.1
Banger Comparisons: 1
Particles $P$ and $Q$, each of mass $m$, lie initially at rest
a distance $a$ apart on a smooth horizontal plane.
They are connected by a light elastic string of natural
length $a$ and modulus of elasticity
$\frac12 m a \omega^2$, where $\omega$ is a constant.
Then $P$ receives an impulse which gives it a
velocity $u$ directly away from $Q$. Show that when the string
next returns to length $a$, the particles have travelled
a distance $\frac12 \pi u/\omega\,$, and find the speed of
each particle.
Find also the total time between the impulse and the subsequent
collision of the particles.
Just under a quarter of candidates offered something on this, with relatively little success and less than 20 candidates earning good marks. As with question 9, it tended to be a case of "all or nothing". Of the good solutions, half based their working on the motion of and relative to the centre of mass of the system, and the other half on setting up simultaneous differential equations for the displacements of the particles. Of the poor attempts, most usually drew some kind of diagram, but then didn't use it to identify a sensible coordinate system, or positive direction, and there were common confusions over displacements x and extensions x. Energy approaches usually got nowhere.