Pulling the tablecloth

Problem

Pulling the tablecloth. A magician quickly pulls the tablecloth out from under the plates without tipping them over. Explain in five lines which physical principle makes the trick possible.

Solution

The trick is explained by inertia (first law) and by the impulse–momentum relation. While the tablecloth slides away, the only horizontal force on the plates is the tablecloth-plate friction, which acts only for the very brief instant $\Delta t$ during which the tablecloth is still beneath them. The impulse transmitted to each plate is $F\,\Delta t$, and the plate’s change in velocity is

$\Delta v = \frac{F\,\Delta t}{m}$

If the pull is fast enough, $\Delta t$ is tiny: the impulse $F\,\Delta t$ is negligible and the plates acquire an almost-zero velocity change $\Delta v$. By inertia they remain practically still while the cloth slips out. A slow motion, on the other hand, lengthens $\Delta t$, increases the impulse, and the plates get dragged along.

$\ev{\Delta v = \dfrac{F\,\Delta t}{m}\to 0 \text{ if } \Delta t \text{ is small: the plates stay still by inertia.}}$

Links

Topics: Dynamics Concepts: Newton’s first law · Impulse