M1 January 2010 Q3

Figure 1: particle C hanging from strings AC and BC attached to a horizontal ceiling, AC at 30 degrees and BC at 60 degrees to the ceiling — Figure 1

A particle of mass \(m\) kg is attached at \(C\) to two light inextensible strings \(AC\) and \(BC\). The other ends of the strings are attached to fixed points \(A\) and \(B\) on a horizontal ceiling. The particle hangs in equilibrium with \(AC\) and \(BC\) inclined to the horizontal at 30\(^\circ\) and 60\(^\circ\) respectively, as shown in Figure 1.

Given that the tension in \(AC\) is 20 N, find

(a) the tension in \(BC\), (4)

(b) the value of \(m\). (4)

Scheme	Marks
R\((\rightarrow)\) \(20\cos 30^\circ = T\cos 60^\circ\)	M1 A2 (1,0)
\(T = 20\sqrt{3}\), 34.6, 34.64,…	A1
	(4)

Scheme	Marks
R\((\uparrow)\) \(mg = 20\sin 30^\circ + T\sin 60^\circ\)	M1 A2 (1,0)
\(m = \dfrac{40}{g}\ (\approx 4.1)\), 4.08	A1
	(4)
	(8 marks)