M1 June 2008 Q6

EdexcelOld spec10 marksMoments

Figure 2: horizontal plank AB of length 2.4 m held by vertical ropes at A and B, with a load at C where AC = 0.8 m — Figure 2

A plank \(AB\) has mass 12 kg and length 2.4 m. A load of mass 8 kg is attached to the plank at the point \(C\), where \(AC = 0.8\) m. The loaded plank is held in equilibrium, with \(AB\) horizontal, by two vertical ropes, one attached at \(A\) and the other attached at \(B\), as shown in Figure 2. The plank is modelled as a uniform rod, the load as a particle and the ropes as light inextensible strings.

(a) Find the tension in the rope attached at \(B\). (4)

The plank is now modelled as a non-uniform rod. With the new model, the tension in the rope attached at \(A\) is 10 N greater than the tension in the rope attached at \(B\).

(b) Find the distance of the centre of mass of the plank from \(A\). (6)

Force diagram: tension X + 10 at A and X at B, 8g at 0.8 from A and 12g at distance x from A — Mark scheme (b)

Scheme	Marks
\(M(A)\ \ \ 8g \times 0.8 + 12g \times 1.2 = X \times 2.4\)	M1 A1
\(X \approx 85\ \ (\text{N})\) accept 84.9, \(\dfrac{26g}{3}\)	DM1 A1
	(4)

Scheme	Marks
\(R(\uparrow)\ \ \ \underline{(X + 10)} + \underline{X} = 8g + 12g\) \((X = 93)\)	M1 B1 A1
\(M(A)\ \ \ 8g \times 0.8 + 12g \times x = X \times 2.4\)	M1 A1
\(x = 1.4\ \ (\text{m})\) accept 1.36	A1
	(6)
	(10 marks)