# Car down hill

Spaceboy
If two cars were at the top of a uniform slope, and the cars are identical in every way other than their mass, which one would reach the bottom first? and why?

This is an argument that lasted all the way from inverness to dundee, and still hasn't been settled, even though there are about 100 people involved now. I need someone to settle it before it escalates further.

I personally think the lighter one would get to the bottom first as the friction would be greater for the heavier one from the tires being spread; although I'm not sure if the momentum of the heavier car, once it picked up some speed, would outweigh friction and air resistance.

avarmaavarma
The lighter one I would think

The frictional force is the only difference on the two cars - and it should be higher on the heavier car. Therefore the lighter car should move faster (less resistance). The AIR RESISTANCE is identical on the two cars - since it depends on surface area exposed to the air (that is why a parachute can stop a fall).

Consider the extreme case when the incline is a level surface - and the cars are attached to an ELASTIC pulling them towards a wall. Which car would smash into the wall first? The lighter one - cause it will encounter less resistance on its way to being pulled.

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Homework Helper
Aerodynamic drag versus weight is lower for the heavier car. If the speeds get high enough that aerodynamic drag is the main limiting factor, then the heavier car is faster. As an extreme example, imagine two identically shaped objects in "free fall" in the atmoshpere, the heavier object has a higher terminal velocity.

avarmaavarma
Hmmm - I agree with the heavier object having higher terminal velocity.
However - 'terminal velocity' means that the acceleration has stopped - the drag force is equal to the weight of the object - it is no longer accelerating.

I don't think cars rolling down a hill will achieve terminal velocity. They will be at speeds well below terminal velocities. So - while there will be a drag force (which will depend on their exposed surface area to the air) - it should be the same on both of them.
The frictional force however - should be dependent on their mass - and the heavier one should feel more resistance from the road.