M2 June 2013 (R) Q1

EdexcelOld spec7 marksPower

1. A caravan of mass 600 kg is towed by a car of mass 900 kg along a straight horizontal road. The towbar joining the car to the caravan is modelled as a light rod parallel to the road. The total resistance to motion of the car is modelled as having magnitude 300 N. The total resistance to motion of the caravan is modelled as having magnitude 150 N. At a given instant the car and the caravan are moving with speed 20 m s\(^{-1}\) and acceleration 0.2 m s\(^{-2}\).

(a) Find the power being developed by the car’s engine at this instant. (5)

(b) Find the tension in the towbar at this instant. (2)

Mark scheme (a)

Scheme	Marks
\(F - 150 - 300 = 1500 \times 0.2\)	M1 A1
\(F = 750\)	A1
\(P = 750 \times 20 = 15000\) watts	M1 A1
	(5)

Notes

M1 Needs total mass and both resistances. Condone sign errors

A1 Correct unsimplified equation

M1 Independent M. 20 x their driving force

Mark scheme (b)

Use their mass as a guide to which of these two alternatives is being used.

Scheme	Marks
For caravan: \(T - 150 = 600 \times 0.2\)	M1
\(T = 270\) N	A1
	(2)
	(7 marks)

Notes

M1 Requires all forces acting on caravan. Condone sign error(s)

Or (b)

For car: \(F - T - 300 = 900 \times 0.2\)	M1
\(T = 270\) N	A1

M1 Requires all forces acting on car. Condone sign error(s)