| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | January |
| 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 a point and applying equilibrium conditions. Part (a) is routine calculation, parts (b-c) involve the common 'point of tilting' scenario. While multi-part with 10 marks total, each step follows textbook methods with no novel insight required, making it slightly easier than average. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force6.04a Centre of mass: gravitational effect6.04b Find centre of mass: using symmetry |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(M(C): 80 \times x = 120 \times 0.5\) → \(x = 0.75\) | M1 A1 | cso |
| (b) Using reaction at \(C = 0\): \(M(D): 120 \times 0.25 = W \times 1.25\) → \(W = 24\) (N) | B1 M1 A1 | ft their \(x\) |
| (c) \(X = 24 + 120 = 144\) (N) | M1 A1 | ft their \(W\) |
| (d) The weight of the rock acts precisely at \(B\) | B1 | 1 mark |
**(a)** $M(C): 80 \times x = 120 \times 0.5$ → $x = 0.75$ | M1 A1 | cso | 3 marks
**(b)** Using reaction at $C = 0$: $M(D): 120 \times 0.25 = W \times 1.25$ → $W = 24$ (N) | B1 M1 A1 | ft their $x$ | 4 marks
**(c)** $X = 24 + 120 = 144$ (N) | M1 A1 | ft their $W$ | 2 marks
**(d)** The weight of the rock acts precisely at $B$ | B1 | 1 mark | 10 marks total
---\includegraphics{figure_2}
A uniform plank $AB$ has weight 120 N and length 3 m. The plank rests horizontally in equilibrium on two smooth supports $C$ and $D$, where $AC = 1$ m and $CD = x$ m, as shown in Figure 2. The reaction of the support on the plank at $D$ has magnitude 80 N. Modelling the plank as a rod,
\begin{enumerate}[label=(\alph*)]
\item show that $x = 0.75$ [3]
\end{enumerate}
A rock is now placed at $B$ and the plank is on the point of tilting about $D$. Modelling the rock as a particle, find
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the weight of the rock, [4]
\item the magnitude of the reaction of the support on the plank at $D$. [2]
\item State how you have used the model of the rock as a particle. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2007 Q2 [10]}}