This is not a question but a general doubt. So if a sphere is kept on an inclined plane what would be its potential energy.Will it be mgh or mg(h+r). I need to use it in derivation (final velocity at bottom when rolling) kindly help me. thanks
$\begingroup$
$\endgroup$
1
-
1$\begingroup$ When completely rolled down, the center of mass will still be $r$ abover the surface, so the difference in height is $h$ $\endgroup$– jng224Commented Feb 25, 2021 at 13:26
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
If $h$ is the height of the point of contact P of the sphere with the ramp, and the angle of the ramp is $\theta$, then $$ V = mgh+ m\,r\cos \theta $$ as the centre of the mass O of the ball is not directly over $x$ because PO is perpendiculr to the ramp surface.
As @Jonas has said, the $r\cos \theta$ does not change with $h$ so if your are interested only in changes of $V$ it is irrelevelent.
answered Feb 25, 2021 at 13:26