Wheels and bumps

Originally posted by uzless
Edit (my suspicion here is that the wheel can't get over a ramp height higher than 50% of the radius....based on nothing but gut instinct)

Well, my revised calculation (for a frictionless contact) gives a limitation of:

h < R[1 - sqrt(c/1+c)]

Suggesting you're right for an elastic collision (in fact the limit is even lower), but for a perfectly inelastic collision it's always possible if V is high enough.

To be perfectly honest, I have no idea what the answer to this is. I was just putting it out there. I was trying to solve it myself using force/momentum balances and moments, but I'm obviously a bit rusty because I'm not getting anywhere. I'm not sure how to deal with the time element in the balance F(x) = d(mv(x))/dt, although I'm sure there's something clever I'm missing.

Some interesting points were brought up, though. What is the nature of the interaction at the point of contact? One force will be directed through the wheel's centre, but must there necessarily be a frictional component to provide lift? And what would the magnitude of the developed force be? Is it possible to calculate it without assuming some sort of compression of the wheel over a specified time interval? Inquiring minds want to know.