M1 June 2007 Q3

EdexcelOld spec9 marksMoments

Figure 2: horizontal rod AB of length 1.5 m with a particle at B, supported at C where AC = 0.9 m — Figure 2

A uniform rod \(AB\) has length 1.5 m and mass 8 kg. A particle of mass \(m\) kg is attached to the rod at \(B\). The rod is supported at the point \(C\), where \(AC = 0.9\) m, and the system is in equilibrium with \(AB\) horizontal, as shown in Figure 2.

(a) Show that \(m = 2\). (4)

A particle of mass 5 kg is now attached to the rod at \(A\) and the support is moved from \(C\) to a point \(D\) of the rod. The system, including both particles, is again in equilibrium with \(AB\) horizontal.

(b) Find the distance \(AD\). (5)

Scheme	Marks
M\((C)\) \(8g \times (0.9 - 0.75) = mg(1.5 - 0.9)\)	M1 A1
Solving to \(m = 2\) \(\ast\) cso	DM1 A1
	(4)

Scheme	Marks
M\((D)\) \(5g \times x = 8g \times (0.75 - x) + 2g(1.5 - x)\)	M1 A2(1, 0)
Solving to \(x = 0.6\) \((AD = 0.6\text{ m})\)	DM1 A1
	(5)
	(9 marks)