| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Beam suspended by vertical ropes |
| Difficulty | Standard +0.3 This is a standard M1 moments problem requiring taking moments about a point, resolving vertically, and applying equilibrium conditions. The multi-part structure and algebraic manipulation add some length, but the techniques are routine and well-practiced in M1 courses with no novel insight required. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks |
|---|---|
| (a) \(M(S): a \times 4g = 2a \times R_T + a \times xg\) | M1 A1 A1 |
| \(+ a: 2R_T = 4g - xg = (4-x)g\) | M1 A1 |
| \(R_T = (2 - \frac{1}{2}x)g\) | |
| \(R_S = (4 + x)g - (2 - \frac{1}{2}x)g = (2 + \frac{3}{2}x)g\) | M1 A1 |
| (b) \(R_S = 5R_T\): \(2 + 1.5x = 10 - 2.5x\) | M1 A1 A1 |
| \(4x = 8\) | |
| \(x = 2\) | |
| (c) When \(R_T = 0\), \(x = 4\) | M1 A1 |
| Total: 12 marks |
(a) $M(S): a \times 4g = 2a \times R_T + a \times xg$ | M1 A1 A1 |
| $+ a: 2R_T = 4g - xg = (4-x)g$ | M1 A1 |
| $R_T = (2 - \frac{1}{2}x)g$ | |
| $R_S = (4 + x)g - (2 - \frac{1}{2}x)g = (2 + \frac{3}{2}x)g$ | M1 A1 |
(b) $R_S = 5R_T$: $2 + 1.5x = 10 - 2.5x$ | M1 A1 A1 |
| $4x = 8$ | |
| $x = 2$ | |
(c) When $R_T = 0$, $x = 4$ | M1 A1 |
| | **Total: 12 marks**A uniform yoke $AB$, of mass 4 kg and length 4$a$ m, rests on the shoulders $S$ and $T$ of two oxen. $AS = TB = a$ m. A bucket of mass $x$ kg is suspended from $A$.
\includegraphics{figure_4}
\begin{enumerate}[label=(\alph*)]
\item Show that the vertical force on the yoke at $T$ has magnitude $(2 - \frac{1}{4}x)g$ N and find, in terms of $x$ and $g$, the vertical force on the yoke at $S$. [7 marks]
\item If the ratio of these vertical forces is $5 : 1$, find the value of $x$. [3 marks]
\item Find the maximum value of $x$ for which the yoke will remain horizontal. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [12]}}