Car towing trailer, inclined road

A question is this type if and only if it involves a car towing a trailer up or down a slope, requiring Newton's second law applied to the system and/or individual vehicles on an inclined plane.

6 questions · Standard +0.3

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CAIE M1 2020 Specimen Q5
9 marks Standard +0.3
5 A car of mass 1200 kg is pulling a trailer of mass 800 kg up a hill inclined at an angle of \(\sin ^ { - 1 } ( 0.1 )\) to the horizontal. The car and the trailer are connected by a light rigid tow-bar which is parallel to the road. The driving force of the car's engine is 2500 N and the resistances to the car and trailer are 300 N and 100 N respectively.
  1. Find the acceleration of the system and the tension in the tow-bar.
  2. When the car and trailer are travelling at a speed of \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the driving force becomes zero. Find the time, in seconds, before the system comes to rest and the force in the tow-bar during this time.
CAIE M1 2016 March Q5
7 marks Standard +0.3
5 A car of mass 1200 kg is pulling a trailer of mass 800 kg up a hill inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.1\). The system of the car and the trailer is modelled as two particles connected by a light inextensible cable. The driving force of the car's engine is 2500 N and the resistances to the car and trailer are 100 N and 150 N respectively.
  1. Find the acceleration of the system and the tension in the cable.
  2. When the car and trailer are travelling at a speed of \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the driving force becomes zero. The cable remains taut. Find the time, in seconds, before the system comes to rest.
Edexcel M1 2020 June Q6
8 marks Standard +0.3
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05cf68a3-1ba4-487f-9edd-48a246f4194f-20_328_1082_127_438} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A railway engine of mass 1500 kg is attached to a railway truck of mass 500 kg by a straight rigid coupling. The engine pushes the truck up a straight track, which is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 7 } { 25 }\). The coupling is parallel to the track and parallel to the direction of motion, as shown in Figure 3. The engine produces a constant driving force of magnitude \(D\) newtons. The engine and the truck experience constant resistances to motion, from non-gravitational forces, of magnitude 1200 N and 500 N respectively. The thrust in the coupling is 2000 N . The coupling is modelled as a light rod.
  1. Find the acceleration of the engine and the truck.
  2. Find the value of \(D\).
Edexcel M1 2023 June Q7
11 marks Standard +0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2737a11-4a15-41e9-9f87-31a705a8948b-18_326_1107_246_479} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} A car of mass 1200 kg is towing a trailer of mass 600 kg up a straight road, as shown in Figure 4. The road is inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 12 }\) The driving force produced by the engine of the car is 3000 N .
The car moves with acceleration \(0.75 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) The non-gravitational resistance to motion of
  • the car is modelled as a constant force of magnitude \(2 R\) newtons
  • the trailer is modelled as a constant force of magnitude \(R\) newtons
The car and the trailer are modelled as particles.
The tow bar between the car and trailer is modelled as a light rod that is parallel to the direction of motion. Using the model,
  1. show that the value of \(R\) is 60
  2. find the tension in the tow bar. When the car and trailer are moving at a speed of \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the tow bar breaks.
    Given that the non-gravitational resistance to motion of the trailer remains unchanged,
  3. use the model to find the further distance moved by the trailer before it first comes to rest.
CAIE M1 2024 March Q6
10 marks Standard +0.3
A car of mass 1800 kg is towing a trailer of mass 300 kg up a straight road inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.05\). The car and trailer are connected by a tow-bar which is light and rigid and is parallel to the road. There is a resistance force of 800 N acting on the car and a resistance force of \(F\) N acting on the trailer. The driving force of the car's engine is 3000 N.
  1. It is given that \(F = 100\). Find the acceleration of the car and the tension in the tow-bar. [5]
  2. It is given instead that the total work done against \(F\) in moving a distance of 50 m up the road is 6000 J. The speed of the car at the start of the 50 m is \(20\) m s\(^{-1}\). Use an energy method to find the speed of the car at the end of the 50 m. [5]
CAIE M1 2020 November Q6
9 marks Standard +0.3
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 \(30 \text{ m s}^{-1}\) at the bottom of the hill and \(20 \text{ m s}^{-1}\) 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. [5]
  2. 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]