A solid 0.6350 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.6350 m. What minimum translational speed ?min must the ball have when it is a height ?=0.9944 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius ?. Use ?=9.810 m/s^2 for the acceleration due to gravity.

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A solid 0.6350 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.6350 m. What minimum translational speed ?min must the ball have when it is a height ?=0.9944 m above the bottom of the loop in order to complete the loop without falling off the track?

Assume that the radius of the ball itself is much smaller than the loop radius ?. Use ?=9.810 m/s^2 for the acceleration due to gravity.

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At the top of circular track loop 

N+mg=mv2RAs, the rolling of solid ball without slipping is in anticlock wise direction,so, normal force will be balanced by centrifugal forcefor critical condition when it leaves contact to surface,N=0mv2=mgRfrrom conservation of energy, PEi+KEi=PEf+KEfmgH+12mv2min+1225MR2ω2min=mg2R+12mv2+1225MR2ω2since we know v=ωRon solving we get,vmin=mg2710R-H710m1/2putting the value we getm=0.6350 kgR=0.6350H=0.9944mvmin=21.765 vmin=4.66 m/s

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