A-LevelMathematicsMechanics9709/41 · Oct/Nov 2018 · Q24 Marks
A high-speed train of mass 490 000 kg is moving along a straight horizontal track at a constant speed of 85 m s⁻¹. The engines are supplying 4080 kW of power.
- (i)Show that the resistance force is 48 000 N.[1]
- (ii)The train comes to a hill inclined at an angle θ° above the horizontal, where sin θ° = 1/200. Given that the resistance force is unchanged, find the power required for the train to keep moving at the same constant speed of 85 m s⁻¹.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] Correct use of P = Fv and using DF = Resistance
- [B1] DF = P/v
- [M1] For applying Newton's second law (3 terms)
- [A1] P = 72 500 × 85 = 6.16 MW
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