A-LevelMathematicsMechanics9709/41 · Oct/Nov 2017 · Q36 Marks

A roller-coaster car (including passengers) has a mass of 840 kg. The roller-coaster ride includes a section where the car climbs a straight ramp of length 8 m inclined at 30° above the horizontal. The car then immediately descends another ramp of length 10m inclined at 20° below the horizontal. The resistance to motion acting on the car is 640 N throughout the motion.

(i)Find the total work done against the resistance force as the car ascends the first ramp and descends the second ramp.[2]
(ii)The speed of the car at the bottom of the first ramp is 14 m s⁻¹. Use an energy method to find the speed of the car when it reaches the bottom of the second ramp.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[M1] 640 × 18 For use of work done = F × d
[A1] Work done = 11 520 J
[B1] KE at start = ½ × 840 × 14² = 82 320 J
[B1] PE gained = 840g × 8sin 30 - 840g × 10sin 20 = 4870 J
[M1] ½ × 840 × v² = 82 320 – 11 520 – 4870 For using work – energy equation with 4 terms and solving for v
[A1] v = 12.5 m s⁻¹

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