A-LevelMathematicsMechanics9709/42 · Feb/Mar 2023 · Q47 Marks

A toy railway locomotive of mass 0.8kg is towing a truck of mass 0.4kg on a straight horizontal track at a constant speed of 2ms⁻¹. There is a constant resistance force of magnitude 0.2N on the locomotive, but no resistance force on the truck. There is a light rigid horizontal coupling connecting the locomotive and the truck.

(a)State the tension in the coupling.[1]
(b)Find the power produced by the locomotive's engine.[1]
(c)The power produced by the locomotive's engine is now changed to 1.2 W. Find the magnitude of the tension in the coupling at the instant that the locomotive begins to accelerate.[5]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

[B1] Tension = 0N May be implied.
[B1] Power [=0.2×2] = 0.4 W Use of power = Fv. Allow without units.
[B1] Driving force = 1.2/2 [= 0.6 N]
[M1] Use of Newton's second law for locomotive or truck or system Correct number of relevant terms.
[A1] For any two correct. For locomotive: DF - 0.2-T=0.8a For truck: T=0.4a For system: DF-0.2=1.2a
[M1] For attempt to solve for T From equations with correct number of relevant terms. Using their dimensionally correct DF. May see a = 1/3
[A1] T=2/15 N Allow awrt 0.133.

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