M3 January 2005 Q1

EdexcelOld spec7 marksHorizontal Circular Motion

1. A particle \(P\) of mass 0.5 kg is attached to one end of a light inextensible string of length 1.5 m. The other end of the string is attached to a fixed point \(A\). The particle is moving, with the string taut, in a horizontal circle with centre \(O\) vertically below \(A\). The particle is moving with constant angular speed 2.7 rad s\(^{-1}\). Find

(a) the tension in the string, (4)

(b) the angle, to the nearest degree, that \(AP\) makes with the downward vertical. (3)

Scheme	Marks
\(r = 1.5\sin\theta\)	B1
\(T\sin\theta = mr\omega^2\)	M1 A1
\(T\sin\theta = 0.5 \times 1.5\sin\theta \times 2.7^2\)
\(T = 5.4675\) N	A1
	(4)

Scheme	Marks
\(T\cos\theta = 0.5g\)	M1 A1
\(\cos\theta = \dfrac{0.5g}{5.4675}\)
\(\theta = 26^\circ\) (nearest degree)	A1
	(3)
	(7 marks)