M1 January 2011 Q3

EdexcelOld spec10 marksMoments

Figure 1: beam AB of length 6 m on supports at C, 1 m from A, and at B — Figure 1

A uniform beam \(AB\) has mass 20 kg and length 6 m. The beam rests in equilibrium in a horizontal position on two smooth supports. One support is at \(C\), where \(AC = 1\) m, and the other is at the end \(B\), as shown in Figure 1. The beam is modelled as a rod.

(a) Find the magnitudes of the reactions on the beam at \(B\) and at \(C\). (5)

A boy of mass 30 kg stands on the beam at the point \(D\). The beam remains in equilibrium. The magnitudes of the reactions on the beam at \(B\) and at \(C\) are now equal. The boy is modelled as a particle.

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

Force diagram: R_C up at C (1 m from A), 20g down 2 m from C, R_B up at B (3 m further) — Mark scheme (a)

Force diagram: as in (a) with 30g down at distance x from A — Mark scheme (b)

Scheme	Marks
Taking moments about B: \(5 \times R_C = 20g \times 3\)	M1A1
\(R_C = 12g\) or \(60g/5\) or 118 or 120	A1
Resolving vertically: \(R_C + R_B = 20g\)	M1
\(R_B = 8g\) or 78.4 or 78	A1
	(5)

Scheme	Marks
Resolving vertically: \(50g = R + R\)	B1
Taking moments about B:
\(5 \times 25g = 3 \times 20g + (6 - x) \times 30g\)	M1 A1 A1
\(30x = 115\)
\(x = 3.8\) or better or \(23/6\) oe	A1
	(5)
	(10 marks)