When we are trying to find the speed that a cart can complete on a loop, such that it barely is able to make it (or if we are spinning a bucket and we want to know the minimum speed so that none of the water falls), we do we set the normal force equal to 0? I'm having a hard time understanding this concept. Thanks.
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The centripetal force at the top of the loop has to equal (or exceed) the gravity force (weight) of the object. Otherwise the water falls out of the bucket or the cart lifts off the track (although the track should have retainers if it is well designed!).
mv^2/r >= mg
or v^2/r >= g
mv^2/r >= mg
or v^2/r >= g
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You would set the normal force to be 0 at the top of the arc. That is, the centripetal force would just balance the weight of the water and hence it would not "fall" out of the bucket.
At the bottom of the arc, the centripital force would then be added to the weight of the water for a 2X weight
Astrobuf
At the bottom of the arc, the centripital force would then be added to the weight of the water for a 2X weight
Astrobuf