Moderate -0.5 This is a standard two-string equilibrium problem requiring resolution of forces in two directions and solving simultaneous equations. While it involves trigonometry and careful algebraic manipulation, it's a routine textbook exercise with a well-established method (resolve horizontally and vertically, then solve). Slightly easier than average due to being a direct application of a standard technique with no conceptual challenges.
2
\includegraphics[max width=\textwidth, alt={}, center]{f1f33ef0-0d4d-4a4a-aadb-28de8dc0ea8d-03_280_588_264_774}
A particle of mass 2.4 kg is held in equilibrium by two light inextensible strings, one of which is attached to point \(A\) and the other attached to point \(B\). The strings make angles of \(35 ^ { \circ }\) and \(40 ^ { \circ }\) with the horizontal (see diagram).
Find the tension in each of the two strings.
Attempt to resolve horizontally or vertically to form an equation.
\*M1
Correct number of terms; allow sin/cos mix; allow sign errors – do not award this mark if using \(T\) for both (see SC later).
\(T_1\cos 35 = T_2\cos 40\)
A1
Must be different \(T\)s.
\(T_1\sin 35 + T_2\sin 40 = 2.4g\)
A1
If same \(T\)s, then SC B2 only for this equation.
Attempt to solve for either tension.
DM1
From equations with correct number of relevant terms. Must get a value for at least one tension. E.g. \(T_2\left(\frac{\cos 40}{\cos 35}\times\sin 35 + \sin 40\right) = 24\)
\(T_1 = 20.4\text{ N}\) and \(T_2 = 19.0\text{ N}\)
A1
\(T_1 = 19.033621...\) \(T_2 = 20.353166...\) awrt 20.4 for \(T_1\) www and 19(.0) for \(T_2\).
5
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Attempt to resolve horizontally or vertically to form an equation. | **\*M1** | Correct number of terms; allow sin/cos mix; allow sign errors – do not award this mark if using $T$ for both (see **SC** later). |
| $T_1\cos 35 = T_2\cos 40$ | **A1** | Must be different $T$s. |
| $T_1\sin 35 + T_2\sin 40 = 2.4g$ | **A1** | If same $T$s, then **SC B2** only for this equation. |
| Attempt to solve for either tension. | **DM1** | From equations with correct number of relevant terms. Must get a value for at least one tension. E.g. $T_2\left(\frac{\cos 40}{\cos 35}\times\sin 35 + \sin 40\right) = 24$ |
| $T_1 = 20.4\text{ N}$ and $T_2 = 19.0\text{ N}$ | **A1** | $T_1 = 19.033621...$ $T_2 = 20.353166...$ awrt 20.4 for $T_1$ www and 19(.0) for $T_2$. |
| | **5** | |
2\\
\includegraphics[max width=\textwidth, alt={}, center]{f1f33ef0-0d4d-4a4a-aadb-28de8dc0ea8d-03_280_588_264_774}
A particle of mass 2.4 kg is held in equilibrium by two light inextensible strings, one of which is attached to point $A$ and the other attached to point $B$. The strings make angles of $35 ^ { \circ }$ and $40 ^ { \circ }$ with the horizontal (see diagram).
Find the tension in each of the two strings.\\
\hfill \mbox{\textit{CAIE M1 2023 Q2 [5]}}