When the quarter jumps into a cup (and when it does not)

TL;DR

This paper critically examines a popular physics demonstration involving a coin and a cup, showing that the common Bernoulli's equation explanation is flawed and clarifying the actual physics behind the coin's movement.

Contribution

It adapts a demonstration to distinguish when Bernoulli's equation applies and when it does not, correcting a widespread misconception in physics education.

Findings

Demonstrates cases where the coin jumps into the cup and where it does not

Shows Bernoulli's equation is incorrectly used to explain the phenomenon

Clarifies the actual physics principles involved

Abstract

While Bernoulli's equation is one of the most frequently mentioned topics in Physics literature and other means of dissemination, it is also one of the least understood. Oddly enough, in the wonderful book "Turning the world inside out" [1], Robert Ehrlich proposes a demonstration that consists of blowing a quarter dollar coin into a cup, incorrectly explained using Bernoulli's equation. In the present work, we have adapted the demonstration to show situations in which the coin jumps into the cup and others in which it does not, proving that the explanation based on Bernoulli's is flawed. Our demonstration is useful to tackle the common misconception, stemming from the incorrect use of Bernoulli's equation, that higher velocity invariably means lower pressure.