| Exam Board | OCR MEI |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2007 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Variable Force |
| Type | Variable mass problems (mass increasing) |
| Difficulty | Challenging +1.2 This is a standard variable mass problem requiring application of momentum conservation (coal falls vertically, so no horizontal momentum added). Part (i) involves straightforward integration after setting up the momentum equation, while part (ii) requires substituting v=u/2 into the given formula. The conceptual setup is moderately challenging but the mathematical execution is routine for M4 students. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.06a Variable force: dv/dt or v*dv/dx methods |
2 A railway truck of mass $m _ { 0 }$ travels along a horizontal track. There is no driving force and the resistances to motion are negligible. The truck is being filled with coal which falls vertically into it at a mass rate $k$. The process starts as the truck passes a point O with speed $u$. After time $t$, the truck has velocity $v$ and the displacement from O is $x$.\\
(i) Show that $v = \frac { m _ { 0 } u } { m _ { 0 } + k t }$ and find $x$ in terms of $m _ { 0 } , u , k$ and $t$.\\
(ii) Find the distance that the truck has travelled when its speed has been halved.
\hfill \mbox{\textit{OCR MEI M4 2007 Q2 [12]}}