| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Non-uniform beam on supports |
| Difficulty | Standard +0.3 This is a straightforward moments problem requiring two equilibrium equations (vertical forces and moments about a point). The setup is clear, the algebra is simple, and it follows a standard M1 template for non-uniform rods. Slightly easier than average due to its routine nature and minimal computational complexity. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(R = 5g + 8g = 13g = 127.4 \text{ N}\) | M1 A1 | |
| (b) \(M(x): 5g \cdot d + 8g \cdot 4a = 13g \times 3a\); \(5d = 7a\); \(d = 1.4a\) | M1 A1 A1 | 5 marks |
(a) $R = 5g + 8g = 13g = 127.4 \text{ N}$ | M1 A1 |
(b) $M(x): 5g \cdot d + 8g \cdot 4a = 13g \times 3a$; $5d = 7a$; $d = 1.4a$ | M1 A1 A1 | 5 marks2. A plank of wood $X Y$ has length $5 a$ m and mass 5 kg . It rests on a support at $Q$, where $X Q = 3 a$\\
m . When a kitten of mass 8 kg sits on the plank at $P$, where $P Y = a \mathrm {~m}$, the plank just remains horizontal.
By modelling the plank as a non-uniform rod and the kitten as a particle, find
\begin{enumerate}[label=(\alph*)]
\item the magnitude of the reaction at the support,
\item the distance from $X$ to the centre of mass of the plank, in terms of $a$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [5]}}