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Mar31-12, 10:17 AM
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Quote Quote by sgstudent View Post
… in this link: I don't quite understand what direction the friction will be since its just rolling down. In this case would the wheels friction be like the barked ones or the non brakes ones? And why can't I include them into my work done against/by friction? I read somewhere that its because its static friction so it works only at each individual points so there is no distance like in the work done=force x distance formula. But then again, why would this be static friction and not kinetic friction/sliding friction?
your link says …
The force of friction does not do work upon the cart because it acts upon the wheels of the cart and actually does not serve to displace either the cart nor the wheels.

The friction force only serves to help the wheels turn as the cart rolls down the hill.

Friction only does work upon a skidding wheel.
… i've read something like this many times, but it's wrong!

friction (from the road) does do work on a rolling wheel …

in the obvious case of an accelerating car on a horizontal road, the only external horizontal force is the friction (from the road) …
if it's not doing the work, what is??!!
work done = force "dot" displacement of the point of application of the force, the point of application is the point of contact with the road, and that's moving!

suppose the car has mass M, and the wheels have total mass m radius r and total moment of inertia I …

if a horizontal force P pushes the car (on a horizontal road), and if the total friction force is F, and if the reaction force between the car and the wheels is R, then …
P - F = (M+m)a

Fr = Ia/r

so P - (I/r2)a = (M+m)a,

or P = (M+m+mr)a, where mr is the "rolling mass" I/r2
in other words: either we must take F (the friction) into account, or we must add the "rolling mass" to the actual mass of the wheels and the car