A-LevelMathematicsMechanics9709/41 · Oct/Nov 2020 · Q69 Marks

A car of mass 1500 kg is pulling a trailer of mass 750 kg up a straight hill of length 800 m inclined at an angle of sin⁻¹ 0.08 to the horizontal. The resistances to the motion of the car and trailer are 400 N and 200 N respectively. The car and trailer are connected by a light rigid tow-bar. The car and trailer have speed 30 m s⁻¹ at the bottom of the hill and 20 m s⁻¹ at the top of the hill.

(a)Use an energy method to find the constant driving force as the car and trailer travel up the hill.[5]
(b)After reaching the top of the hill the system consisting of the car and trailer travels along a straight level road. The driving force of the car's engine is 2400 N and the resistances to motion are unchanged. Find the acceleration of the system and the tension in the tow-bar.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[B1] Use KE = ½mv² for any two of the four elements
[B1] PE gain = 2250 × 10 × 800 × 0.08
[B1] WD against friction = 600 × 800
[M1] Use energy equation.
[A1] DF = 1700 N
[M1] Apply Newton's second law to the system or to each of the car and trailer separately
[A1] Two correct equations
[M1] Attempting to solve for a or for T
[A1] T = 800 N and a = 0.8 ms⁻²

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