M1 June 2007 Q1

Figure 1: particle P on a string from O at 20 degrees to the downward vertical, with a horizontal force of 12 N at P — Figure 1

A particle \(P\) is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point \(O\). A horizontal force of magnitude 12 N is applied to \(P\). The particle \(P\) is in equilibrium with the string taut and \(OP\) making an angle of 20\(^\circ\) with the downward vertical, as shown in Figure 1.

Find

(a) the tension in the string, (3)

(b) the weight of \(P\). (4)

Scheme	Marks
\(\rightarrow\ \ T\sin 20^\circ = 12\)	M1 A1
\(T \approx 35.1\ \ (\text{N})\) awrt 35	A1
	(3)

Scheme	Marks
\(\uparrow\ \ W = T\cos 20^\circ\)	M1 A1
\(\approx 33.0\ \ (\text{N})\) awrt 33	DM1 A1
	(4)
	(7 marks)