| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Moments |
| Type | Beam on point of tilting |
| Difficulty | Standard +0.3 This is a standard A-level mechanics question on moments and equilibrium. Parts (i)-(iii) involve straightforward applications of resolving forces vertically and taking moments about a point - routine techniques that follow directly from the setup. Part (iv) asks for standard modeling limitations. While it requires careful working through multiple parts, each step uses well-practiced methods without requiring novel insight or complex problem-solving. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks |
|---|---|
| \(25\text{N}\) | B1 [1] |
| Answer | Marks | Guidance |
|---|---|---|
| \(2(100) = 75x + (x+0.5)(25)\) | A1ft | Follow through their 25 only |
| \(x = 1.875\) | A1 [3] | eg moments about \(A\) – correct number of terms |
| Answer | Marks | Guidance |
|---|---|---|
| \((x + 0.5 - 2)(100) = W(4 - 0.5 - x)\) | A1ft | Follow through their \(x\) only |
| \(W = 23.1\text{N}\) | A1 [3] | Accept 23 or better; moments about \(D\) – correct number of terms |
## Question 9:
### Part (i):
$25\text{N}$ | B1 [1] | |
### Part (ii):
$2(100) = 75x + (x+0.5)(25)$ | A1ft | Follow through their 25 only |
$x = 1.875$ | A1 [3] | eg moments about $A$ – correct number of terms |
### Part (iii):
$(x + 0.5 - 2)(100) = W(4 - 0.5 - x)$ | A1ft | Follow through their $x$ only |
$W = 23.1\text{N}$ | A1 [3] | Accept 23 or better; moments about $D$ – correct number of terms |
---9 A uniform plank $A B$ has weight 100 N and length 4 m . The plank rests horizontally in equilibrium on two smooth supports $C$ and $D$, where $A C = x \mathrm {~m}$ and $C D = 0.5 \mathrm {~m}$ (see diagram).\\
\includegraphics[max width=\textwidth, alt={}, center]{d5ab20c8-afd5-473e-8238-96762bd3786d-6_181_1271_1101_395}
The magnitude of the reaction of the support on the plank at $C$ is 75 N . Modelling the plank as a rigid rod, find\\
(i) the magnitude of the reaction of the support on the plank at $D$,\\
(ii) the value of $x$.
A stone block, which is modelled as a particle, is now placed at the end of the plank at $B$ and the plank is on the point of tilting about $D$.\\
(iii) Find the weight of the stone block.\\
(iv) Explain the limitation of modelling
\begin{enumerate}[label=(\alph*)]
\item the stone block as a particle,
\item the plank as a rigid rod.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2018 Q9 [9]}}