| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | October |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Uniform beam on two supports |
| Difficulty | Moderate -0.3 This is a standard M1 moments problem requiring equilibrium conditions (sum of moments = 0, sum of vertical forces = 0) with straightforward algebra. The setup is clear, involving a uniform beam with two supports and one additional mass. While it requires careful bookkeeping of distances and forces, it follows a routine textbook approach with no conceptual surprises, making it slightly easier than average. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \((\uparrow)\quad R + 2R = 12g + 3g\) | M1 A2 | Vertical resolution; correct terms; \(-1\) each error |
| \(M(A),\quad 2Rx + 3R = 12g(4) + 3g(8)\) | M1 A2 | Moments equation; all terms dimensionally correct |
| \(x = 5.7\) | A1 (7) |
## Question 3:
| Working | Marks | Guidance |
|---------|-------|---------|
| $(\uparrow)\quad R + 2R = 12g + 3g$ | M1 A2 | Vertical resolution; correct terms; $-1$ each error |
| $M(A),\quad 2Rx + 3R = 12g(4) + 3g(8)$ | M1 A2 | Moments equation; all terms dimensionally correct |
| $x = 5.7$ | A1 (7) | |
*Additional moments equations noted:*
- $M(B),\ R \times 5 + S(8-x) = 12g \times 4$
- $M(C),\ S(x-3) = 12g \times 1 + 3g \times 5$
- $M(D),\ R(x-3) + 3g(8-x) = 12g(x-4)$
---3.
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A plank $A B$ has length 8 m and mass 12 kg . The plank rests on two supports. One support is at $C$, where $A C = 3 \mathrm {~m}$ and the other support is at $D$, where $A D = x$ metres. A block of mass 3 kg is placed on the plank at $B$, as shown in Figure 1. The plank rests in equilibrium in a horizontal position. The magnitude of the force exerted on the plank by the support at $D$ is twice the magnitude of the force exerted on the plank by the support at $C$. The plank is modelled as a uniform rod and the block is modelled as a particle.
Find the value of $x$.\\
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\hfill \mbox{\textit{Edexcel M1 2016 Q3 [7]}}