| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Uniform beam on two supports |
| Difficulty | Moderate -0.3 This is a standard M1 moments equilibrium problem with a uniform rod and point masses. It requires taking moments about a point and resolving vertically—routine techniques taught early in the mechanics course. The setup is straightforward with no geometric complexity or novel insight required, making it slightly easier than average but still requiring proper method. |
| Spec | 3.04b Equilibrium: zero resultant moment and force3.04c Use moments: beams, ladders, static problems |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Moments about \(P\): \(4g + 8g = 2kg\) | \(k = 6\) | M1 A1 A1 |
| (b) Resolve vertically: \(R = 9g + kg\) | \(R = 15g = 147 \text{ N}\) | M1 A1 |
(a) Moments about $P$: $4g + 8g = 2kg$ | $k = 6$ | M1 A1 A1
(b) Resolve vertically: $R = 9g + kg$ | $R = 15g = 147 \text{ N}$ | M1 A1 | **5 marks**A plank of wood $AB$, of mass 8 kg and length 6 m, rests on a support at $P$, where $AP = 4$ m. When particles of mass 1 kg and $k$ kg are suspended from $A$ and $B$ respectively, the plank rests horizontally in equilibrium.
Modelling the plank as a uniform rod, find
\begin{enumerate}[label=(\alph*)]
\item the value of $k$, [3 marks]
\item the magnitude of the force exerted by the support on the plank at $P$. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q1 [5]}}