M1 January 2005 Q2

EdexcelOld spec7 marksMoments

Figure 1: horizontal plank AB of length 3 m held by vertical ropes at A and C, load at B — Figure 1

A plank \(AB\) has mass 40 kg and length 3 m. A load of mass 20 kg is attached to the plank at \(B\). The loaded plank is held in equilibrium, with \(AB\) horizontal, by two vertical ropes attached at \(A\) and \(C\), as shown in Figure 1. The plank is modelled as a uniform rod and the load as a particle. Given that the tension in the rope at \(C\) is three times the tension in the rope at \(A\), calculate

(a) the tension in the rope at \(C\), (2)

(b) the distance \(CB\). (5)

Scheme	Marks
R(\(\uparrow\)): \(T + 3T = 40g + 20g\)	M1
\(T = 15g\), so tension at \(C\) is \(45g\) or 441 N or 440 N	A1
	(2)

Scheme	Marks
M(\(B\)) \(15g \times 3 + 45g \times d = 40g \times 1.5\)	M1 A2,1,0ft
Solve: \(d = 1/3\) or 0.33 or 0.333 m	M1 A1
	(5)
	(7 marks)