The minimum condition ensuring that the water does not fall out of the bucket is centripetal force of the bucket must be equal to sum of tension on the rope and weight of the bucket [tex]( \frac{mv^2}{r} = T + mg )[/tex].
Tension on top of a vertical circle
The tension on top of a vertical circle is given as follows;
[tex]T = F_c - W\\\\T = \frac{mv^2}{r} - mg[/tex]
[tex]T + mg = \frac{mv^2}{r}[/tex]
where;
- m is the mass of the bucket
- T is the tension on the rope
- r is the length of the rope forming radius of circular path
- v is the speed of the bucket
- g is acceleration due to gravity
Thus, the minimum condition ensuring that the water does not fall out of the bucket is centripetal force of the bucket must be equal to sum of tension on the rope and weight of the bucket.
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