Vehicle pulling trailer - tension

A question is this type if and only if it involves a car/lorry pulling a trailer with a towbar, asking for tension in the connection or acceleration of the system.

2 questions · Moderate -0.3

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CAIE M1 2019 March Q4
7 marks Moderate -0.3
A car of mass \(1500\) kg is pulling a trailer of mass \(300\) kg along a straight horizontal road at a constant speed of \(20\) m s\(^{-1}\). The system of the car and trailer is modelled as two particles, connected by a light rigid horizontal rod. The power of the car's engine is \(6000\) W. There are constant resistances to motion of \(R\) N on the car and \(80\) N on the trailer.
  1. Find the value of \(R\). [2]
  2. The power of the car's engine is increased to \(12\,500\) W. The resistance forces do not change. Find the acceleration of the car and trailer and the tension in the rod at an instant when the speed of the car is \(25\) m s\(^{-1}\). [5]
Edexcel M2 2013 June Q1
7 marks Moderate -0.3
A caravan of mass 600 kg is towed by a car of mass 900 kg along a straight horizontal road. The towbar joining the car to the caravan is modelled as a light rod parallel to the road. The total resistance to motion of the car is modelled as having magnitude 300 N. The total resistance to motion of the caravan is modelled as having magnitude 150 N. At a given instant the car and the caravan are moving with speed 20 m s\(^{-1}\) and acceleration 0.2 m s\(^{-2}\).
  1. Find the power being developed by the car's engine at this instant. [5]
  2. Find the tension in the towbar at this instant. [2]