How Is Work Calculated on a Conveyor Belt with Friction?

[haruspex]

for a work is done because it gains GPE

Read post #6 again.
In a, work mgh is done by the belt and work -mgh is done by gravity. But the question asks about work done on the case: mgh+(-mgh)=0.

 

[haruspex]

they didn’t mean frictionless belt

and, indeed, did not say frictionless belt. They wrote no "resistive forces opposing motion", which is ambiguous. The motion could mean the actual velocity of the case up the ramp (the friction does not oppose that) or it could be taken as the motion that would occur were there no friction: acceleration down the ramp.

 

[erobz]

and, indeed, did not say frictionless belt. They wrote no "resistive forces opposing motion", which is ambiguous. The motion could mean the actual velocity of the case up the ramp (the friction does not oppose that) or it could be taken as the motion that would occur were there no friction: acceleration down the ramp.

I agree, but I think they meant there is friction between the belt and the box, and there is no “drag” type forces.

 

[haruspex]

I agree, but I think they meant there is friction between the belt and the box, and there is no “drag” type forces.

Oh yes, that is what was meant, no question.