| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Beam on point of tilting |
| Difficulty | Moderate -0.3 This is a standard M1 moments question requiring taking moments about two points and resolving vertically. The setup is straightforward with clearly defined forces and distances. Part (a) uses routine equilibrium equations, part (b) applies the same method with an inequality, and part (c) tests understanding of modelling assumptions. While it requires careful calculation across multiple parts (6+3+1=10 marks), it involves no novel problem-solving—just systematic application of standard moments techniques taught in every M1 course. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
\includegraphics{figure_1}
A diving board $AB$ consists of a wooden plank of length 4 m and mass 30 kg. The plank is held at rest in a horizontal position by two supports at the points $A$ and $C$, where $AC = 0.6$ m, as shown in Figure 1. The force on the plank at $A$ acts vertically downwards and the force on the plank at $C$ acts vertically upwards.
A diver of mass 50 kg is standing on the board at the end $B$. The diver is modelled as a particle and the plank is modelled as a uniform rod. The plank is in equilibrium.
\begin{enumerate}[label=(\alph*)]
\item Find
\begin{enumerate}[label=(\roman*)]
\item the magnitude of the force acting on the plank at $A$,
\item the magnitude of the force acting on the plank at $C$.
\end{enumerate}
[6]
The support at $A$ will break if subjected to a force whose magnitude is greater than 5000 N.
\item Find, in kg, the greatest integer mass of a diver who can stand on the board at $B$ without breaking the support at $A$.
[3]
\item Explain how you have used the fact that the diver is modelled as a particle.
[1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2016 Q4 [10]}}