| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2004 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle suspended by strings |
| Difficulty | Moderate -0.8 This is a standard two-string equilibrium problem requiring resolution of forces in two perpendicular directions. Students apply routine methods (resolving horizontally and vertically) with given angles and one tension to find the other tension and weight. It's more straightforward than average A-level questions since the setup is simple, angles are standard (30° and 60°), and the method is well-practiced in M1. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks |
|---|---|
| 1 | T (a) R (→): T cos 60 = 50 cos 30 M1 A1 |
Question 1:
1 | T (a) R (→): T cos 60 = 50 cos 30 M1 A1
50
T = 86.6 N A1
(3)
W
(b) R(↑): W = 50 sin 30 + T cos 30 M1 A1
= 100 N A1
(3)
or R ( to BC): W cos 60 = 50 M1 A1
W = 100 N A1
(3)
(a) M1 for a valid equation in T only
Treat use of tan 30/60 (e.g. tan 30 = T/50) as invalid equation unless there is a triangle of
Forces
(b) M1 for a valid equation involving W (and T if necessary)
for first A1 in (i), allow for using their T (i.e. effectively f.t.)
Accept each answer as awrt.\includegraphics{figure_1}
A particle of weight $W$ newtons is attached at $C$ to the ends of two light inextensible strings $AC$ and $BC$. The other ends of the strings are attached to two fixed points $A$ and $B$ on a horizontal ceiling. The particle hangs in equilibrium with $AC$ and $BC$ inclined to the horizontal at $30°$ and $60°$ respectively, as shown in Fig. 1. Given the tension in $AC$ is 50 N, calculate
\begin{enumerate}[label=(\alph*)]
\item the tension in $BC$, to 3 significant figures, [3]
\item the value of $W$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2004 Q1 [6]}}