| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2010 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | Particle on outer surface of cylinder |
| Difficulty | Challenging +1.2 This is a classic particle-on-cylinder problem requiring energy conservation, circular motion dynamics, and numerical solution of a transcendental equation. While it involves multiple steps and careful manipulation of forces/energy, it follows a standard M3 template with clear signposting through parts (i)-(iii). The numerical iteration in part (iii) is routine for this level. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.05d Variable speed circles: energy methods |
(i) By considering the total energy of the system, obtain an expression for $v ^ { 2 }$ in terms of $\theta$.\\
(ii) Show that the magnitude of the force exerted on $P$ by the cylinder is $( 7.12 \sin \theta - 4.64 \theta ) \mathrm { N }$.\\
(iii) Given that $P$ leaves the surface of the cylinder when $\theta = \alpha$, show that $1.53 < \alpha < 1.54$.
\hfill \mbox{\textit{OCR M3 2010 Q6 [13]}}