Question

A physics teacher swings a pail of water in a vertical circle 5.0 ft. in a radius at constant speed. (a) What is the speed of the pail of water? (b) What is the maximum time per revolution if the water is not to spill?

Answer 1

At the top of the circle, gravity must act completely as a centripetal force.\[\underbrace{\cancel mg}_{\text{gravity}}=\underbrace{\frac{\cancel mv^2}{r}}_{\text{centripetal}}\Rightarrow \boxed{v=\sqrt{rg}}\]Since constant velocity is defined by \(v=\frac{\Delta x}{\Delta t}\), we can say the following based on what we know about the geometry of the system. We can use our found value for \(v\) to find \(\Delta t\). \[v=\frac{2\pi r}{\Delta t} \Rightarrow \boxed{\displaystyle \Delta t = 2\pi \sqrt{\frac{r}{g}}}\]

Answer 2

Again, plug in your given values.