A small mass m slides without friction along the looped apparatus shown in Fig. 6-39. If the object is to remain on the track, even at the top of the circle (whose radius is r), from what minimum height h must it be released? (Answer in terms of r.)

Answer 1

I can only imagine what the figure is, and my crystal ball is not working.

I assume h is measured from the bottom of the loop, so the PE going into the mass is h-2r measured at the top. So that is equal to KE at the top.

mg(h-2r)=1/2 m v^2
so solve that for v^2

Now, at the top, the force on the track is mg-mv^2/r, and that to stay on the track must be non negative.0<mg-mv^2/r
so put in v^2 from before, and solve for h.

Answer 2

Thanks that helps alot