| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle suspended by strings |
| Difficulty | Moderate -0.3 This is a standard M1 equilibrium problem requiring resolution of forces in two directions with straightforward trigonometry. While it involves three forces and two angles, the method is routine (resolve horizontally and vertically, solve simultaneous equations). Part (b) requires minimal physical insight about symmetry. Slightly easier than average due to being a textbook application of equilibrium principles. |
| Spec | 3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| (a) resolve \(\uparrow\): \(T_1\sin35° + T_2\sin40° - 0.7g = 0\) (1) | M1 A1 | |
| resolve \(\rightarrow\): \(T_2\cos40° - T_1\cos35° = 0\) (2) | M1 | |
| from (2), \(T_2 = 1.069 T_1\) | M1 | |
| sub. into (1) to get \(T_1 = 5.44 \text{ N}\) (3sf) | M1 A1 | |
| and so \(T_2 = 5.82 \text{ N}\) | A1 | |
| (b) e.g. jacket likely to slide to a position near centre of line | B1 | (8) |
(a) resolve $\uparrow$: $T_1\sin35° + T_2\sin40° - 0.7g = 0$ (1) | M1 A1 |
resolve $\rightarrow$: $T_2\cos40° - T_1\cos35° = 0$ (2) | M1 |
from (2), $T_2 = 1.069 T_1$ | M1 |
sub. into (1) to get $T_1 = 5.44 \text{ N}$ (3sf) | M1 A1 |
and so $T_2 = 5.82 \text{ N}$ | A1 |
(b) e.g. jacket likely to slide to a position near centre of line | B1 | (8) |2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{8a0ff401-83da-4539-a9e9-68736c57df2a-2_291_613_1599_516}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
Figure 2 shows a washing line suspended at either end by vertical rigid poles. A jacket of mass 0.7 kg is suspended in equilibrium part of the way along the line. The sections of the washing line on either side of the jacket make angles of $35 ^ { \circ }$ and $40 ^ { \circ }$ with the horizontal.
\begin{enumerate}[label=(\alph*)]
\item Find the tension in the washing line on each side of the jacket.
\item Explain why, in practice, the angles are likely to be very similar in value.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [8]}}