Acceleration and center of gravity question?

Question

This is not a homework problem so don't worry, more a personal observation...

Why would a go-cart with it's center of gravity closer to the front end accelerate faster than the same cart with the center of gravity near the rear given both are sent down the same hill at the same time? What forces at work would cause this discrepancy?

Answer 1

I'm not necessarily sure that I agree with your observation, that the object accelerates any faster. The acceleration of an object down a hill has nothing to do with its position on the hill. For instance, if the hill is at an angle of pi/4 from the horizon, the downward acceleration on that object will be g cos (pi/4). Notice that mass and position are not in play here.

However, if your question asks why the go cart is traveling faster at the bottom of the hill, the solution may be a little different. Actually, the following reason disagrees with your observation. If the center of mass is towards the back of the go cart, the object has a slightly higher potential energy. By the bottom of the hill, all that potential energy should have been converted into translational kinetic energy (I'll ignore the rolling wheels for right now). The larger potential energy gives rise to a larger kinetic energy, thus a higher velocity. I would then say that the go cart with the center of mass near the rear should end up going faster.

Answer 2

Hi. Did you observe this? I would think it was the other way around because the rear CG would have more potential energy. At least that's how I instructed my son when he built a pine-wood derby car.