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Suppposing the same enviroment conditions and without considering the air friction a car at the start of a race would have a greater acceleration on Earth or on the Moon, or would the accelerations be equal?

It's a trivial question but I'm having troubles to understand the real reason why the acceleration would be greater on Earth.

The propulsion of the car is caused by friction with the Earth/Moon surface but I can't relate that to the mass of the planet, but just to the mass of the car, since $F= m_{CAR} . a_{CAR}$ and it seems to be indipendent by the mass of the planet.

What am I missing here?

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  • $\begingroup$ This type of question has been asked many times. But obvious answer comes out to be "depends on conditions". $\endgroup$ – Anubhav Goel Feb 7 '16 at 11:32
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If we assume all other things being equal other than the downward force due to gravity, the vehicle on Earth would be capable of greater acceleration.

The ability of the tires to grip the surface on which they are resting depends on the downward force keeping them in contact (Coefficient of friction). That will pretty much relate the gravitational acceleration of the planet (or moon) to the maximum acceleration a vehicle can achieve along a level road.

This is why drag racers are always rear-wheel drive. The torque reaction when accelerating shifts the weight distribution of the car rearward, reducing the available traction on the front wheels while increasing it on the rear wheels. It's also why people used to put bags of sand in the trunk of their cars (back when they were all rear-wheel drive) to increase the weight and therefore available traction in snowy conditions (although it was also there to be spread on the snow or ice if needed as a traction aid).

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It is independent of the mass of the planet if you assume the bearings are frictionless. Also assume that the tyres do not make dents in the ground.

However, in reality, the bearings have friction. Additionally, there is rolling resistance as the tyre makes small deformations in the ground as it is rolling. This is why you see a characteristic rounded "W" shape in lanes of roads; over time, the pavement is "compressed" to a point where the pavement that is in contact with wheels all the time sinks down.

Now, to friction in the bearings. Since the moon is less massive than earth, objects of the same mass will weigh less on the moon than on the earth. Therefore, there will be a greater normal force in the bearings if the car is on Earth, which means more frictional torque is generated and more engine torque is needed to overcome the static friction forces.

In the end, it really depends on the properties of the ground materials. For example, dirt has more rolling resistance than asphalt/tarmac or concrete.

Hope this helps.

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