Question

A bucket of water can be whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explain.

Short answer

The amount of water will remain the same in the bucket, even if it is moving in a vertical circle.

Step-by-step solution

Step 1. Understanding the forces acting on the bucket

In this problem, at the top of the circle the forces exerting in downward direction are normal force and force due of gravity. Also, these forces will produce a centripetal force to keep the water moving.

Step 2. Explaining the reason behind whirling a bucket of water in a vertical circle without the water spitting out

The relation from Newton’s second law can be given as,

$\begin{array}{c}F=mg\\ \frac{m{v}^2}{r}=mg\\ v=\sqrt{rg}\end{array}$

Here, F is the force, m is the mass, g is the gravitational acceleration, v is the speed and r is the radius.

Now, the speed of the water inside the bucket should be more than or equal to $v=\sqrt{rg}$ for protecting the water from spilling out. At the top of the vertical circle, the water has a horizontal velocity, and as the bucket crosses the top section, it will develop a vertical velocity. However, the bucket is moving with an identical velocity and consists of the water as it drops within the rest of its route.