M2 June 2008 Q1

EdexcelOld spec6 marksPower

1. A lorry of mass 2000 kg is moving down a straight road inclined at angle \(\alpha\) to the horizontal, where \(\sin\alpha = \dfrac{1}{25}\). The resistance to motion is modelled as a constant force of magnitude 1600 N. The lorry is moving at a constant speed of 14 m s\(^{-1}\).

Find, in kW, the rate at which the lorry’s engine is working. (6)

Force diagram: Tr down the slope, 1600 up the slope, 2000g vertically down — Mark scheme

Scheme	Marks
Resolve \(\nearrow\): \(\ T_r + \underline{2000g \times \sin\alpha} = 1600\)	M1 A1 A1
\((T_r = 816)\)
\(P = 816 \times 14\) (W) ft their \(T_r\)	M1 A1ft
\(\approx 11\) (kW) accept 11.4	A1 cso
	(6)
	(6 marks)