| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | June |
| Marks | 7 |
| 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 to find tensions, then finding the limiting case where one tension becomes zero. It involves straightforward application of equilibrium conditions with multiple forces, slightly above average due to the two-part structure and the limiting case in part (b), but still a routine textbook-style question with no novel insight required. |
| Spec | 3.04b Equilibrium: zero resultant moment and force3.04c Use moments: beams, ladders, static problems |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(M(D)\): \((150g \times 1) + (60g \times 2.5) = Tc \times 4\) | M1 A1 | M1 for complete method to find \(Tc\) (M0 if \(T_C = T_D\) assumed). Equation must have correct no. of terms and be dimensionally correct |
| \(Tc = 75g\) or \(735\) N or \(740\) N | A1 (3) | Allow omission of N |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(M(B)\): \((150g \times 4.5) + (60g \times 6) = T_D \times 3.5\) | M1 A2 | M1 for complete method for equation in \(T_D\) only. A1A0 if one error. Note: M0 if \(T_C\) is ever equated to 0 |
| \(T_D = 2900\) N or \(\frac{2070g}{7}\) | A1 (4) | Allow omission of N |
# Question 3:
## Part (a):
| Working | Marks | Guidance |
|---------|-------|----------|
| $M(D)$: $(150g \times 1) + (60g \times 2.5) = Tc \times 4$ | M1 A1 | M1 for complete method to find $Tc$ (M0 if $T_C = T_D$ assumed). Equation must have correct no. of terms and be dimensionally correct |
| $Tc = 75g$ or $735$ N or $740$ N | A1 (3) | Allow omission of N |
## Part (b):
| Working | Marks | Guidance |
|---------|-------|----------|
| $M(B)$: $(150g \times 4.5) + (60g \times 6) = T_D \times 3.5$ | M1 A2 | M1 for complete method for equation in $T_D$ only. A1A0 if one error. Note: M0 if $T_C$ is ever equated to 0 |
| $T_D = 2900$ N or $\frac{2070g}{7}$ | A1 (4) | Allow omission of N |
**Total: (7)**
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{4fd21e83-0bdf-4bb1-8a3f-76beada511ae-08_426_1226_221_360}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
A wooden beam $A B$, of mass 150 kg and length 9 m , rests in a horizontal position supported by two vertical ropes. The ropes are attached to the beam at $C$ and $D$, where $A C = 1.5 \mathrm {~m}$ and $B D = 3.5 \mathrm {~m}$. A gymnast of mass 60 kg stands on the beam at the point $P$, where $A P = 3 \mathrm {~m}$, as shown in Figure 2. The beam remains horizontal and in equilibrium.
By modelling the gymnast as a particle, the beam as a uniform rod and the ropes as light inextensible strings,
\begin{enumerate}[label=(\alph*)]
\item find the tension in the rope attached to the beam at $C$.
The gymnast at $P$ remains on the beam at $P$ and another gymnast, who is also modelled as a particle, stands on the beam at $B$. The beam remains horizontal and in equilibrium. The mass of the gymnast at $B$ is the largest possible for which the beam remains horizontal and in equilibrium.
\item Find the tension in the rope attached to the beam at $D$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2018 Q3 [7]}}