Sliding without friction pedagogy

[houlahound]

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.

 

[Simon Bridge]

Over what you did? No. Not really.
With wheels you have rolling resistance, and some of the potential energy gets stored as rotation in the wheels ... to improve matters you have to use harder, smaller, lighter wheels - and a harder surface. Minimising deformation minimises rolling resistance (means harder surfaces), and lower moment of inertia (means lower radius and mass) means less energy goes to turning the wheels.

What you can do is make the mass of the car very big compared to the wheels so the amount of KE taken turning the wheels is small in proportion. This is why the standard physics trolleys are the way they are. If the cars are about 200-500g and the wheels are small aluminium disks, you can get within the kind of uncertainties that students produce for the frictionless situation.

The "meter ruler and stopwatch" uncertainties are your friend here.

 

[CWatters]

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.

You can measure the friction and use it to calculate how much longer the cart/block will take to slide down compared to the no-friction case. Is that what you mean?