# Towing a caravan

## Question:

1. A car of mass 1500 kg is towing a caravan with a mass of 1000 kg with an acceleration of 1 ms-2. Assuming that the only external force on the system is that between the driving wheels and the road.
Find:-
(a) the value of this force
(b) the tension in the coupling between the car and the caravan
(c) the resultant force on the car.

## Answer:

A car of mass 1500 kg pulls a caravan of mass 1000 kg
Call the accelerating force (the force between the driving wheels and the road) F
(a) Use F = Ma where M is the total mass in other words the mass of the car and the caravan because both are being accelerated.
Acceleration = 1 ms-2 and the total mass is (1500 + 1000) = 2500 kg
Therefore: F = (1500 + 1000) x 1 = 2500 N

However the caravan must have the same acceleration as the car otherwise they would separate or squash together.
(b) So accelerating force in the caravan alone (this is the tension in the coupling) = T
T = ma = 1000x 1 = 1000 N
(c) By Newton's third law when two bodies are in equilibrium (in this case the car and the caravan) when a force acts on one body an equal and opposite force acts on the other body.

Therefore: Force on the car = tension in the coupling = 1000 N

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© Keith Gibbs 2020