| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Uniform beam on two supports |
| Difficulty | Standard +0.3 This is a standard M1 moments problem requiring equilibrium equations (sum of forces and taking moments about a point) with straightforward algebra. The setup is clear, the constraint (reaction at C is 5 times reaction at A) provides the key relationship, and the calculations are routine for this topic. Slightly above average difficulty due to the algebraic manipulation with the variable x appearing twice, but still a typical textbook-style mechanics question. |
| Spec | 3.04b Equilibrium: zero resultant moment and force3.04c Use moments: beams, ladders, static problems |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \((\uparrow)\; R + 5R = 75g + 30g + 75g\) | M1 A2 | M1 for vertical resolution with correct terms; A1A1 for correct equation (\(-1\) each error) |
| \(M(A)\; 75gx + 75g \cdot 2x + 30g \times 3 = 5R \times 4\) | M1 A2 | M1 for moments equation, all terms dimensionally correct; A1A1 for correct equation |
| \(x = \frac{34}{15} = 2.3\) (or better) | A1 (7) | Any equivalent form |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| uniform – mass acts at midpoint of plank; centre of mass is at middle of plank | B1 | First correct answer |
| rod – plank does not bend; remains straight; is inflexible; is rigid | B1 (2) | Second B1 only if no extras given |
# Question 3:
## Part (a):
| Working/Answer | Marks | Guidance |
|---|---|---|
| $(\uparrow)\; R + 5R = 75g + 30g + 75g$ | M1 A2 | M1 for vertical resolution with correct terms; A1A1 for correct equation ($-1$ each error) |
| $M(A)\; 75gx + 75g \cdot 2x + 30g \times 3 = 5R \times 4$ | M1 A2 | M1 for moments equation, all terms dimensionally correct; A1A1 for correct equation |
| $x = \frac{34}{15} = 2.3$ (or better) | A1 (7) | Any equivalent form |
## Part (b):
| Working/Answer | Marks | Guidance |
|---|---|---|
| uniform – mass acts at midpoint of plank; centre of mass is at middle of plank | B1 | First correct answer |
| rod – plank does not bend; remains straight; is inflexible; is rigid | B1 (2) | Second B1 only if no extras given |
---3. A plank $A B$ has length 6 m and mass 30 kg . The point $C$ is on the plank with $C B = 2 \mathrm {~m}$. The plank rests in equilibrium in a horizontal position on supports at $A$ and $C$. Two people, each of mass 75 kg , stand on the plank. One person stands at the point $P$ of the plank, where $A P = x$ metres, and the other person stands at the point $Q$ of the plank, where $A Q = 2 x$ metres. The plank remains horizontal and in equilibrium with the magnitude of the reaction at $C$ five times the magnitude of the reaction at $A$. The plank is modelled as a uniform rod and each person is modelled as a particle.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $x$.
\item State two ways in which you have used the assumptions made in modelling the plank as a uniform rod.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2017 Q3 [9]}}