M1 January 2007 Q1

Figure 1: particle with a horizontal string of tension Q N and a string at 30 degrees to the horizontal with tension P N — Figure 1

A particle of weight 24 N is held in equilibrium by two light inextensible strings. One string is horizontal. The other string is inclined at an angle of 30\(^\circ\) to the horizontal, as shown in Figure 1. The tension in the horizontal string is \(Q\) newtons and the tension in the other string is \(P\) newtons. Find

(a) the value of \(P\), (3)

(b) the value of \(Q\). (3)

Scheme	Marks
\(P\sin 30^\circ = 24\)	M1 A1
\(P = 48\)	A1
	(3)

Scheme	Marks
\(Q = P\cos 30^\circ\)	M1 A1
\(\approx 41.6\) accept \(24\sqrt{3}\), awrt 42	A1
	(3)
	(6 marks)