M1 June 2007 Q5

Figure 3: ring on a horizontal rod pulled by a string of tension 1.2 N at 40 degrees above the horizontal — Figure 3

A small ring of mass 0.25 kg is threaded on a fixed rough horizontal rod. The ring is pulled upwards by a light string which makes an angle 40\(^\circ\) with the horizontal, as shown in Figure 3. The string and the rod are in the same vertical plane. The tension in the string is 1.2 N and the coefficient of friction between the ring and the rod is \(\mu\). Given that the ring is in limiting equilibrium, find

(a) the normal reaction between the ring and the rod, (4)

(b) the value of \(\mu\). (6)

Scheme	Marks
\(\uparrow\ \ \pm R + 1.2\sin 40^\circ = 0.25g\)	M1 A1
Solving to \(R = 1.7\ \ (\text{N})\) accept 1.68	DM1 A1
	(4)

Mark scheme (b)

Scheme	Marks
\(\rightarrow\ \ F = 1.2\cos 40^\circ\ \ (\approx 0.919)\)	M1 A1
Use of \(F = \mu R\)	B1
\(1.2\cos 40^\circ = \mu R\) ft their \(R\)	DM1 A1ft
\(\mu \approx 0.55\) accept 0.548	A1 cao
	(6)
	(10 marks)