A variation on Newton's bucket

Classical Mechanics Level 3

Newtonian physics relies on the existence of a preferred inertial reference frame. The existence of such a frame was motivated experimentally by Newton's bucket - the water in a spinning bucket doesn't stay flat but rises closer to the edge. How do you know that the bucket is spinning though (spinning with respect to what)? In Newtonian physics we say that the inertial reference frame is determined by the 'fixed stars'.

A simple problem related to Newton's bucket is the following. Take a hollow cube and fill it half full with water. We smoothly accelerate the bucket to the right with some acceleration \(a\). For what value of \(a\) in \(\text{m/s}^2\) will the water begin to spill out of the bucket?

Details and assumptions

  • The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).

  • There are three distinct ways (at least) to solve this problem. One is brute force, and two are clever.


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