Question

Question #f7ce2

Answer 1

The water in a bucket is most likely to fall when at the highest point in the vertical circle.

The water won't fall if the bucket is made to spin fast enough

That is, its tangential speed(`v`) must be greater than a minimum(which we are going to calculate)

In the first place, for the bucket to describe that circular motion, there must be a centripetal force(`F_c`) and `F_c=(mv^2)/r`

`m` is the combined mass of water plus bucket

`v` is the tangential speed

`r` is the radius of the circle(in this case the length of the rope)

At the highest point this centripetal force is provided by the weight(`mg`) and the tension(`T`)

But `T` tends to zero so,

`(mv^2)/r=mg`

`=>v=sqrt(gr)`

Notice that this velocity is only dependent on the length of the rope used.

In other words it is harder to spin with a longer rope than a shorter rope, because the longer rope requires a higher speed.