| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2010 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Bungee jumping problems |
| Difficulty | Standard +0.8 This is a substantial M3 elastic strings problem requiring energy methods, differentiation of energy to find maximum speed, and force analysis for maximum deceleration. While the techniques are standard for M3, the multi-part structure, careful handling of the piecewise motion (free fall then elastic extension), and the need to find when kinetic energy is maximum (not at lowest point) make this moderately challenging, above average difficulty. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle6.02j Conservation with elastics: springs and strings |
A bungee jumper of weight $W$ N is joined to a fixed point $O$ by a light elastic rope of natural length $20$ m and modulus of elasticity $32\,000$ N. The jumper starts from rest at $O$ and falls vertically. The jumper is modelled as a particle and air resistance is ignored.
\begin{enumerate}[label=(\roman*)]
\item Given that the jumper just reaches a point $25$ m below $O$, find the value of $W$. [5]
\item Find the maximum speed reached by the jumper. [4]
\item Find the maximum value of the deceleration of the jumper during the downward motion. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR M3 2010 Q6 [12]}}