| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Beam on point of tilting |
| Difficulty | Standard +0.3 This is a standard M1 moments question requiring taking moments about a point to find reactions, then finding the limiting position when one reaction becomes zero. The setup is straightforward with clear symmetry, requiring only basic moment equilibrium and resolution of forces—slightly easier than average due to the routine nature of the problem and clear physical setup. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Resolve \(\uparrow\): \(R_1 + R_2 = 135g\) | M1 | |
| Moments about \(A\): \(60g(0.6) - R_2(1.2) + 75g(1.6) = 0\) | M1 A1 | |
| \(1.2R_2 = 156g \therefore R_2 = 130g = 1274\) N | M1 A1 | |
| \(R_1 = 5g = 49\) N | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| When \(R_1 = 0\), moments about \(B\): \(20g(0.6) + 40g(x) - 75g(0.4) = 0\) | M1 A1 | |
| \(12g + 40gx = 30g \therefore 40x = 18\) | A1 | |
| \(x = 0.45\) but \(x\) is dist. L of \(B\) \(\therefore\) Luigi can move to 0.85 m from mother | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Bench is on point of tilting | B1 | (12) |
## Question 6:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Resolve $\uparrow$: $R_1 + R_2 = 135g$ | M1 | |
| Moments about $A$: $60g(0.6) - R_2(1.2) + 75g(1.6) = 0$ | M1 A1 | |
| $1.2R_2 = 156g \therefore R_2 = 130g = 1274$ N | M1 A1 | |
| $R_1 = 5g = 49$ N | A1 | |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| When $R_1 = 0$, moments about $B$: $20g(0.6) + 40g(x) - 75g(0.4) = 0$ | M1 A1 | |
| $12g + 40gx = 30g \therefore 40x = 18$ | A1 | |
| $x = 0.45$ but $x$ is dist. L of $B$ $\therefore$ Luigi can move to 0.85 m from mother | M1 A1 | |
### Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Bench is on point of tilting | B1 | **(12)** |
---6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{6fb27fe5-055a-4701-bd80-e66ebd57292a-4_252_726_194_561}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
Figure 2 shows a picnic bench of mass 20 kg which consists of a horizontal plank of wood of length 2 m resting on two supports, each of which is 0.6 m from the centre of the plank.
Luigi sits on the bench at its midpoint and his mother Maria sits at one end. Their masses are 40 kg and 75 kg respectively.
By modelling the bench as a uniform rod and Luigi and Maria as particles,
\begin{enumerate}[label=(\alph*)]
\item find the reaction at each of the two supports.
Luigi moves to sit closer to his mother.
\item Find how close Luigi can get to his mother before the reaction at one of the supports becomes zero.
\item Explain the significance of a zero reaction at one of the supports.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q6 [12]}}