6 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 \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at the bottom of the hill and \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at the top of the hill.

1. Use an energy method to find the constant driving force as the car and trailer travel up the hill.
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   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.
2. Find the acceleration of the system and the tension in the tow-bar.
   \includegraphics[max width=\textwidth, alt={}, center]{de5edcfa-595b-4a9b-b3b3-7803670759cf-10_440_738_262_699} Three points \(A , B\) and \(C\) lie on a line of greatest slope of a plane inclined at an angle of \(30 ^ { \circ }\) to the horizontal, with \(A B = 1 \mathrm {~m}\) and \(B C = 1 \mathrm {~m}\), as shown in the diagram. A particle of mass 0.2 kg is released from rest at \(A\) and slides down the plane. The part of the plane from \(A\) to \(B\) is smooth. The part of the plane from \(B\) to \(C\) is rough, with coefficient of friction \(\mu\) between the plane and the particle.
3. Given that \(\mu = \frac { 1 } { 2 } \sqrt { 3 }\), find the speed of the particle at \(C\).
4. Given instead that the particle comes to rest at \(C\), find the exact value of \(\mu\).
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