I raced a toy car on a wooden plane alongside an ice cube on a block of ice in my kitchen today. the ice cube combo won every time even allowing for my crude starting gate. most texts I have seen introduce dynamics of inclined planes with a bead on a wire or more common a block on a frictionless surface. I can see how that assumption might be met experimentally on one of those tracks that blow air so there is no contact. more commonly carts are rolled down a plane. is there a way to prove theoretically the magnitude of the discrepancy in results between the no friction assumption and those cart thingy's rolling down the plane.