A crane uses its petrol engine to lift a beam of mass 103 kg by height h. The fuel burned loses 1 MJ (106 J) of chemical potential energy, 85% of this being transferred by heating to the air. The internal energy of the crane’s engine increases by 4.0×104 J, while that of the crane’s superstructure and the beam is unchanged. The crane’s superstructure (not engine or fuel) increases in gravitational potential energy by 104 J. Everything is at rest before and after. Assume all transfer by working out of the crane is used to lift the beam. (a) [10 marks] The calorific value of the fuel is 43 MJ kg−1, its density is 737 kg m−3 and it costs 90p per litre (there are 1000 litres in 1 m3). What was the fuel cost of raising the beam?