Standard +0.3 This is a straightforward 3-force equilibrium problem requiring resolution of forces in two perpendicular directions. Students must find angles using given geometry (Pythagoras), then solve two simultaneous equations. Standard M1 content with clear diagram and no conceptual surprises, making it slightly easier than average.
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\includegraphics[max width=\textwidth, alt={}, center]{139371b7-e142-4ed6-bff3-3ca4c32b9c6b-2_657_913_1450_616}
A particle \(P\) of weight 1.4 N is attached to one end of a light inextensible string \(S _ { 1 }\) of length 1.5 m , and to one end of another light inextensible string \(S _ { 2 }\) of length 1.3 m . The other end of \(S _ { 1 }\) is attached to a wall at the point 0.9 m vertically above a point \(O\) of the wall. The other end of \(S _ { 2 }\) is attached to the wall at the point 0.5 m vertically below \(O\). The particle is held in equilibrium, at the same horizontal level as \(O\), by a horizontal force of magnitude 2.24 N acting away from the wall and perpendicular to it (see diagram). Find the tensions in the strings. [0pt]
[6]
SR for using Lami's Rule for \(T_1, T_2\) and \(2.24\) N (weight missing) (max 3/6): \(T_1/\sin157.38 = 2.24/\sin59.49\) B1; \(T_2/\sin143.13 = 2.24/\sin59.49\) B1; \(T_1 = 1(.00)\) and \(T_2 = 1.56\) B1
## Question 3:
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For resolving forces acting on $P$ horizontally |
| $0.8T_1 + \frac{12T_2}{13} = 2.24$ | A1 | |
| | M1 | For resolving forces acting on $P$ vertically |
| $0.6T_1 - \frac{5T_2}{13} = 1.4$ | A1 | |
| | M1 | For solving for $T_1$ and $T_2$ |
| $T_1 = 2.5$ and $T_2 = 0.26$ | A1 [6] | |
| | | **SR** for using Lami's Rule for $T_1, T_2$ and $2.24$ N (weight missing) (max 3/6): $T_1/\sin157.38 = 2.24/\sin59.49$ B1; $T_2/\sin143.13 = 2.24/\sin59.49$ B1; $T_1 = 1(.00)$ and $T_2 = 1.56$ B1 |
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\includegraphics[max width=\textwidth, alt={}, center]{139371b7-e142-4ed6-bff3-3ca4c32b9c6b-2_657_913_1450_616}
A particle $P$ of weight 1.4 N is attached to one end of a light inextensible string $S _ { 1 }$ of length 1.5 m , and to one end of another light inextensible string $S _ { 2 }$ of length 1.3 m . The other end of $S _ { 1 }$ is attached to a wall at the point 0.9 m vertically above a point $O$ of the wall. The other end of $S _ { 2 }$ is attached to the wall at the point 0.5 m vertically below $O$. The particle is held in equilibrium, at the same horizontal level as $O$, by a horizontal force of magnitude 2.24 N acting away from the wall and perpendicular to it (see diagram). Find the tensions in the strings.\\[0pt]
[6]
\hfill \mbox{\textit{CAIE M1 2014 Q3 [6]}}