Conceptual question; cylinder moving up an inclined plane

[konichiwa2x]

A cylinder rolls up an inclined plane, reaches some height and rolls down (withot slipping throughout these motions). The directions of frictional force acting on the cylinder are : (more than one option may be correct)

(a) Up the incline while ascending and down the incline while descending.
(b) Up the incline while ascending as well as descending.
(c) Down the incline while ascending as well as descending.
(d) Down the incline while ascending as well as descending.

I feel the frictional force should be down the incline while moving up and up the incline while moving down since friction opposes relative motion between the surfaces in contact. But my book says the answer is (B). Is it wrong?

 

[Hootenanny]

Your book is correct. Perhaps if you draw a free body diagram and consider the forces acting on the cylinder the matter may become clearer.

 

[konichiwa2x]

ok I did that. the component of weight of the cylinder along the incline will be mgsin(theta). So since this force always acts down the plane, the frictional force will also always be directed up the incline?

But then, if the cylinder rolls up the incline, isn't there some other force that causes this? I mean, the cylinder will only roll up the incline if that force is greater than mgsin(theta).So the tendency of the cylinder is to move up the incline. and hence frictional force acts down the plane.. Please tell me where I am going wrong.

 

[Hootenanny]

ok I did that. the component of weight of the cylinder along the incline will be mgsin(theta). So since this force always acts down the plane, the frictional force will also always be directed up the incline?

But then, if the cylinder rolls up the incline, isn't there some other force that causes this? I mean, the cylinder will only roll up the incline if that force is greater than mgsin(theta).So the tendency of the cylinder is to move up the incline. and hence frictional force acts down the plane.. Please tell me where I am going wrong.

Where does the question state that there is a force pushing it up the incline? If this was the case why would the cylinder stop and roll back down?

 

[konichiwa2x]

ok I get your point. But then, why does the cylinder roll up the plane in the first place??

 

[Hootenanny]

Imagine the cylinder was set rolling by a force on a smooth horizontal surface, the cylinder then rolls along the surface at constant speed until it meets the incline at which point it experiences a force(s) and thus accelerates (down the incline). Does that make sense?

 

[konichiwa2x]

allright that makes sense. thanks a lot for your help