| Exam Board | OCR |
|---|---|
| Module | Further Mechanics (Further Mechanics) |
| Year | 2021 |
| Session | June |
| Marks | 11 |
| Topic | Projectiles |
| Type | Horizontal projection from height |
| Difficulty | Challenging +1.2 This is a two-part mechanics problem combining circular motion with projectile motion. Part (a) requires applying Newton's second law in circular motion (T - mg cos θ = mv²/r) with energy conservation to find v, which is standard Further Maths technique. Part (b) involves projectile motion from the break point, requiring resolution of velocity and standard SUVAT, but the geometry (finding initial height and horizontal distance from F) adds moderate complexity. While multi-step, each component uses well-practiced methods without requiring novel insight. |
| Spec | 3.02i Projectile motion: constant acceleration model6.02i Conservation of energy: mechanical energy principle6.05d Variable speed circles: energy methods |
2 One end of a light inextensible string of length 0.8 m is attached to a fixed point, $O$. The other end is attached to a particle $P$ of mass $1.2 \mathrm {~kg} . P$ hangs in equilibrium at a distance of 1.5 m above a horizontal plane. The point on the plane directly below $O$ is $F$.\\
$P$ is projected horizontally with speed $3.5 \mathrm {~ms} ^ { - 1 }$. The string breaks when $O P$ makes an angle of $\frac { 1 } { 3 } \pi$ radians with the downwards vertical through $O$ (see diagram).\\
\includegraphics[max width=\textwidth, alt={}, center]{0428f2f2-12c4-4e89-93ab-8cfe2c5aca4a-02_757_889_1482_251}
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of the tension in the string at the instant before the string breaks.
\item Find the distance between $F$ and the point where $P$ first hits the plane.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Mechanics 2021 Q2 [11]}}