| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | June |
| Marks | 7 |
| 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 apply the tilting principle (reaction becomes zero) and take moments about two different points to form simultaneous equations. While it requires careful setup and algebraic manipulation, the method is routine and well-practiced in M1 courses, making it slightly easier than average. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| VIIIV SIHI NI JIIUM ION OC | VIIIV SIHI NI JIIIM ION OC | VI4V SIHI NI JIIYM ION OO |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(M(S): Mg \times 0.5 = 30g(d - 0.5)\) | M1 A1 | Moments about \(S\); correct no. of terms required |
| \(M(T): Mg \times 2 = 30g(4 - d)\) | M1 A1 | Moments about \(T\); correct no. of terms required |
| Dividing: \(4 = \dfrac{(4-d)}{(d-0.5)}\) \(\Rightarrow\) (i) \(d = 1.2\) | DM1 A1 | Dependent on 1st and 2nd M marks; eliminating \(M\) or \(d\); neither A1 can be awarded if errors in equations |
| (ii) \(M = 42\) | A1 |
## Question 6:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $M(S): Mg \times 0.5 = 30g(d - 0.5)$ | M1 A1 | Moments about $S$; correct no. of terms required |
| $M(T): Mg \times 2 = 30g(4 - d)$ | M1 A1 | Moments about $T$; correct no. of terms required |
| Dividing: $4 = \dfrac{(4-d)}{(d-0.5)}$ $\Rightarrow$ (i) $d = 1.2$ | DM1 A1 | Dependent on 1st and 2nd M marks; eliminating $M$ or $d$; neither A1 can be awarded if errors in equations |
| (ii) $M = 42$ | A1 | |
---6. A non-uniform plank $A B$ has length 6 m and mass 30 kg . The plank rests in equilibrium in a horizontal position on supports at the points $S$ and $T$ of the plank where $A S = 0.5 \mathrm {~m}$ and $T B = 2 \mathrm {~m}$.
When a block of mass $M \mathrm {~kg}$ is placed on the plank at $A$, the plank remains horizontal and in equilibrium and the plank is on the point of tilting about $S$.
When the block is moved to $B$, the plank remains horizontal and in equilibrium and the plank is on the point of tilting about $T$.
The distance of the centre of mass of the plank from $A$ is $d$ metres. The block is modelled as a particle and the plank is modelled as a non-uniform rod. Find\\
(i) the value of $d$,\\
(ii) the value of $M$.\\
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VIIIV SIHI NI JIIUM ION OC & VIIIV SIHI NI JIIIM ION OC & VI4V SIHI NI JIIYM ION OO \\
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\hfill \mbox{\textit{Edexcel M1 2016 Q6 [7]}}