## Citroen C3 Swinging Car Advert

This stupid advert has a couple in a Citroen C3 driving in a dockyard and for mischievous fun they decide to swing their car from the cables of a gantry crane using an adapter that just so happens to exactly fit the wheels of their car. The car accelerates, goes up into the air and they swing happily enjoying their shiny new car like it is fairground ride.

I am calling bollocks on this advert and a quick back of the envelope calculation can show why. The relevant physics is that of the pendulum and the conservation of energy. The conservation of energy is very useful in problems like this as it says that the sum of the kinetic energy and the potential energy is a constant.

When the car reaches its maximum height we can say that all its energy is potential energy. Similarly when the car is moving and just about lift off the ground it has it maximum kinetic energy. Anywhere in between there is a mixture of kinetic and potential energy.

At the top of the swing, the potential energy PE = m g h, where m is the mass of the car, g is the acceleration due to gravity and h is the maximum height. Looking at the specifications of the car, the mass is 1360 kg. The height of a gantry crane I would estimate to be about 30 m. In the advert the car seems to go higher than this but let’s be generous and say 30 metres. g is taken as 9.81 m/s^2.

Therefore the potential energy is 400,248 J. The car must have this amount of energy when it takes off also.

The equation for kinetic energy is KE = 0.5 m v^2, where v is the take off velocity. So we can calculate how fast it need to go before it takes off. It turns out that it is around 24.26 m/s or (56 mph).

Looking at the specification of the car it turns out that the 0-100 km take 14.2 sec or an average acceleration of 1.9 m/s^2 so I think that it would need quite a run up to reach this speed.

Remembering my high-school physics of linear motion, the distance required is s = v^2/ 2a, where v is the take off velocity and a is the average acceleration. Plugging in the numbers once again gives a distance of 154 m. Which is substantially longer than the height of the crane. In the advert we only see the car pull back a short distance. Which I think proves the case not to mention that the cable would need to be slackened and then pulled in as the car reaches the take off point which is not going to happen.

Of course with a pendulum or a swing repeated application of energy at just right moment can hit the natural frequency of the pendulum and make the amplitude increase dramatically. However for a car on a crane to do this it would have to go change gear to go into forward and then reverse on the return journey and I don’t think that the car would be able to go that fast in reverse.

I know the advert is made with computer graphics and it is supposed to be describing its big windscreen but it still doesn’t stand up to scruitiny. You might as well say that the car is rocket powered and it can drive in space.

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