| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Beam suspended by vertical ropes |
| Difficulty | Moderate -0.3 This is a standard M1 moments question requiring taking moments about two points to find tensions in terms of x, then solving inequalities. The setup is straightforward with clear given values, and the method is routine for this topic. Slightly easier than average due to being a textbook application of the moments principle with no geometric complications or novel insights required. |
| Spec | 3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks |
|---|---|
| 5(b) | First M1 for their T ≤ 84 or = 84 or < 84 to give equation or inequality in x only. |
Question 5:
--- 5(b) ---
5(b) | First M1 for their T ≤ 84 or = 84 or < 84 to give equation or inequality in x only.
A
(> 84 is M0)
Second M1 for their T ≤ 84 or = 84 or < 84 to give equation or inequality in x
B
only. (> 84 is M0)
First A1 for both critical values of x, 1 and 1.8 SEEN.
Second A1 1 ≤ x ≤ 1.8 or 1 ≤ x AND x ≤ 1.8 or [1, 1.8]\includegraphics{figure_2}
A non-uniform rod $AB$ has length 4 m and weight 120 N. The centre of mass of the rod is at the point $G$ where $AG = 2.2$ m. The rod is suspended in a horizontal position by two vertical light inextensible strings, one at each end, as shown in Figure 2. A particle of weight 40 N is placed on the rod at the point $P$, where $AP = x$ metres. The rod remains horizontal and in equilibrium.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $x$,
\begin{enumerate}[label=(\roman*)]
\item the tension in the string at $A$, [6]
\item the tension in the string at $B$.
\end{enumerate}
Either string will break if the tension in it exceeds 84 N.
\item Find the range of possible values of $x$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2016 Q5 [10]}}