Imagine 2 cars 1 weighs 1 ton, the other weights 2 tons. If we ignore the effect of the suspension – when both of these cars go over the same bump in the road, which accelerates fastest in the vertical direction?
I would have assumed that the lighter car would – as $a=F/m$, so the car with more mass has a lower acceleration. But inversely – would the force input to both cars be the same? Or would this be mass dependent and both cars would accelerate at the same rate?
I guess in simple terms, I'm asking is the force input constant, or is the acceleration constant between the 2 cars – or something in between?
Best Answer
If you ignore the suspension (which is ignoring everything that actually matters) then it makes no difference. As the car goes over the bump it converts kinetic energy it has by virtue of going along the road to vertical kinetic energy and then to potential energy at the top of the bump, and kinetic & potential energy are both proportional to mass, so mass can be factored out and position and all its differentials with respect to time -- in particular velocity and acceleration -- is the same.
But, as I said, don't ignore suspension (or, equivalently, try driving a car with no suspension for a bit and you will quickly understand why you can't ignore it!)