| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2001 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Energy methods in projectiles |
| Difficulty | Challenging +1.2 This is a mechanics problem combining circular motion with projectile motion. Part (a) is straightforward geometry (cos θ = 0.6/0.8). Part (b) requires applying the condition for leaving the surface (normal reaction = 0) and using energy or circular motion principles. Part (c) involves resolving velocity components. While it requires multiple techniques and careful application of leaving-surface conditions, it's a standard M3 question type with clear structure and well-signposted steps, making it moderately above average difficulty. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.05d Variable speed circles: energy methods |
\includegraphics{figure_1}
A smooth solid hemisphere, of radius 0.8 m and centre $O$, is fixed with its plane face on a horizontal table. A particle of mass 0.5 kg is projected horizontally with speed $u$ m s$^{-1}$ from the highest point $A$ of the hemisphere. The particle leaves the hemisphere at the point $B$, which is a vertical distance of 0.2 m below the level of $A$. The speed of the particle at $B$ is $v$ m s$^{-1}$ and the angle between $OA$ and $OB$ is $\theta$, as shown in Fig. 1.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\cos \theta$. [1]
\item Show that $v^2 = 5.88$. [3]
\item Find the value of $u$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2001 Q2 [7]}}