The block of mass m sliding without friction along the looped track s to remain

Question

The block of mass m sliding without friction along the looped track s to remain on the track at all times, even at the very top of the loop of radius r.

a)In terms of the given quantities determine the actual release height h.

b)If the actual release height is 2.7h calculate the normal force exerted by the track at the bottom of the loop.

c)The normal force exerted by the track at the top of the loop

d)The normal force exerted by the track after the block exits the loop onto the flat section.

Please solve in detail thanks!

Explanation / Answer

v^2/r=g so v=sqrt(rg) now mgh =.5*m*v^2 a)so h=r/2 [ r=radius of loop] b) v'=sqrt(2h/g)=sqrt(2.27)*v so F=mv'^2/r + mg=m*(2.27 v^2/r+ g)=m*(3.37 g)=33.026 m

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