| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2021 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Particle suspended by strings |
| Difficulty | Moderate -0.3 This is a standard two-string equilibrium problem requiring resolution of forces in two directions and solving simultaneous equations. While it involves trigonometry and systematic method, it's a routine mechanics exercise with no novel insight required—slightly easier than average due to its textbook nature and straightforward application of equilibrium conditions. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks |
|---|---|
| Correct 3 force diagram, including angles shown | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(T_1 \cos 60 = T_2 \cos 45\) | M1 | Resolving forces horizontally |
| \(T_1 \sin 60 + T_2 \sin 45 = 8g\) | M1 | Resolving forces vertically |
| Both equations correct | A1 | |
| Attempting to solve for either \(T_1\) or \(T_2\) | M1 | |
| \(T_1 = 58.6\) N | A1 | |
| \(T_2 = 41.4\) N | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{T_1}{\sin 135} = \frac{T_2}{\sin 150} = \frac{80}{\sin 75}\) | M1, A1 | Applies Lami's Theorem – at least two terms correct |
| \(T_1 = \frac{80\sin 135}{\sin 75}\) | M1 | Solves for \(T_1\) |
| \(T_1 = 58.6\) N | A1 | |
| \(T_2 = \frac{80\sin 150}{\sin 75}\) | M1 | Solves for \(T_2\) |
| \(T_2 = 41.4\) N | A1 |
## Question 2:
### Part (a):
| Correct 3 force diagram, including angles shown | B1 | |
### Part (b):
| $T_1 \cos 60 = T_2 \cos 45$ | M1 | Resolving forces horizontally |
| $T_1 \sin 60 + T_2 \sin 45 = 8g$ | M1 | Resolving forces vertically |
| Both equations correct | A1 | |
| Attempting to solve for either $T_1$ or $T_2$ | M1 | |
| $T_1 = 58.6$ N | A1 | |
| $T_2 = 41.4$ N | A1 | |
**Alternative method:**
| $\frac{T_1}{\sin 135} = \frac{T_2}{\sin 150} = \frac{80}{\sin 75}$ | M1, A1 | Applies Lami's Theorem – at least two terms correct |
| $T_1 = \frac{80\sin 135}{\sin 75}$ | M1 | Solves for $T_1$ |
| $T_1 = 58.6$ N | A1 | |
| $T_2 = \frac{80\sin 150}{\sin 75}$ | M1 | Solves for $T_2$ |
| $T_2 = 41.4$ N | A1 | |
---2 A particle of mass 8 kg is suspended in equilibrium by two light inextensible strings which make angles of $60 ^ { \circ }$ and $45 ^ { \circ }$ above the horizontal.
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram showing the forces acting on the particle.
\item Find the tensions in the strings.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2021 Q2 [7]}}