M2 January 2010 Q6

EdexcelOld spec7 marksMoments Resolving Forces

Figure 2: rod AB with A on horizontal ground at angle alpha, held by a force at B acting upwards and away from the rod — Figure 2

A uniform rod \(AB\), of mass 20 kg and length 4 m, rests with one end \(A\) on rough horizontal ground. The rod is held in limiting equilibrium at an angle \(\alpha\) to the horizontal, where \(\tan\alpha = \dfrac{3}{4}\), by a force acting at \(B\), as shown in Figure 2. The line of action of this force lies in the vertical plane which contains the rod. The coefficient of friction between the ground and the rod is 0.5. Find the magnitude of the normal reaction of the ground on the rod at \(A\). (7)

Mark scheme

Scheme	Marks
\(m(B):\ R \times 4\cos\alpha = F \times 4\sin\alpha + 20g \times 2\cos\alpha\)	M1 A2
Use of \(\ F = \dfrac{1}{2}R\)	M1
Use of correct trig ratios	B1
\(R = 160\) N or 157 N	DM1 A1
	(7 marks)