A-LevelMathematicsMechanics9709/42 · Feb/Mar 2022 · Q46 Marks

The total mass of a cyclist and her bicycle is 70kg. The cyclist is riding with constant power of 180 W up a straight hill inclined at an angle a to the horizontal, where sin a = 0.05. At an instant when the cyclist's speed is 6ms¯¹, her acceleration is –0.2ms-2. There is a constant resistance to motion of magnitude FN.

(a)Find the value of F.[4]
(b)Find the steady speed that the cyclist could maintain up the hill when working at this power.[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.

[B1] Forward force exerted by cyclist driving force = 180/6 [= 30 N]
[M1] DF - F - 70g sin α = 70 × -0.2 (Attempt Newton's second law, 4 terms required. A value must be used for sin α.)
[A1] 30 - F - 70g × 0.05 = 70 × -0.2 (Correct equation)
[A1] F = 9 (From exact working only)
[M1] 180/v - F - 70g sin α = 0 (Apply Newton's second law up the hill with a = 0. Must have 3 relevant terms using their F from 4(a). A value for sin α must be used.)
[A1] v = 4.09 ms¯¹ (Allow 45/11)

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