| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2021 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Non-uniform beam on supports |
| Difficulty | Standard +0.3 This is a standard M1 moments problem with two equilibrium conditions. Students must set up moments equations about two different pivot points (D and C) using the 'about to tilt' condition (reaction force = 0 at the other support). The algebra is straightforward: two equations, two unknowns (W and x). While it requires understanding of the tilting concept, this is a textbook application of moments with no novel insight needed, making it slightly easier than average. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(M(D),\ 900 \times 5 = W(5-x)\) | M1A1 | Equation in \(W\) and one unknown length, dim correct, condone sign errors. Extra \(g\) on one side is A error. M0 if \(R_C = 0\) never set. Allow consistent use of \(Mg\) for \(W\) |
| \(M(C),\ 1500 \times 5 = W(x-1)\) | M1A1 | Equation in \(W\) and same unknown length, dim correct, condone sign errors. Extra \(g\) on one side is A error. M0 if \(R_D = 0\) never set |
| Solving for \(x\) | DM1 | Dependent on two previous M marks |
| \(x = 3.5\) | A1 | cao, no wrong working seen |
# Question 4:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $M(D),\ 900 \times 5 = W(5-x)$ | M1A1 | Equation in $W$ and one unknown length, dim correct, condone sign errors. Extra $g$ on one side is A error. M0 if $R_C = 0$ never set. Allow consistent use of $Mg$ for $W$ |
| $M(C),\ 1500 \times 5 = W(x-1)$ | M1A1 | Equation in $W$ and same unknown length, dim correct, condone sign errors. Extra $g$ on one side is A error. M0 if $R_D = 0$ never set |
| Solving for $x$ | DM1 | Dependent on two previous M marks |
| $x = 3.5$ | A1 | cao, no wrong working seen |
---4.
\begin{figure}[h]
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\includegraphics[alt={},max width=\textwidth]{ca445c1e-078c-4a57-94df-de90f30f8efd-08_426_1428_118_258}
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\caption{Figure 2}
\end{center}
\end{figure}
\begin{verbatim}
A metal girder $A B$ has weight $W$ newtons and length 6 m . The girder rests in a horizontal position on two supports $C$ and $D$ where $A C = D B = 1 \mathrm {~m}$, as shown in Figure 2.
When a force of magnitude 900 N is applied vertically upwards to the girder at $A$, the girder is about to tilt about $D$.
When a force of magnitude 1500 N is applied vertically upwards to the girder at $B$, the girder is about to tilt about $C$.
The girder is modelled as a non-uniform rod whose centre of mass is a distance $x$ metres from $A$.
Find the value of $x$.
A metal girder AB has weight
When a force of magnitude 1500 N is applied vertically upwards to the girder at $B$, the girder is about to tilt about $C$.
The girder is modelled as a non-uniform rod whose centre of mass is a distance $x$ metres from $A$. Find the value of $x$.
\end{verbatim}
\hfill \mbox{\textit{Edexcel M1 2021 Q4 [6]}}