# Pull the Paper under the Tumbler

## Introduction

Newton's three laws of motion are taught in school from quite early times. Though students know the statements of the three laws but when it comes to application, quite often the laws are wrongly interpreted. The experiment described here is quite common and is shown to dramatize the concept of Newton's 1\textsuperscript{st} law of motion or inertia. However, a detailed analysis reveals greater insight into the laws of motion.

## Procedure

- Near the edge of a table, place a glass tumbler filled with water.
- Now hold the part of the paper overhanging from the table using both hands.
- Give a sharp jerk to the paper and pull it quickly. What you find is that the paper comes out from below the glass and the glass just stays on the table with no water spilling out.
- Try pulling the paper with different speeds and see what happens.

## Discussion

The common explanation is that because of inertia, the glass remains at its place and the paper comes out. But is it the explanation? Where does this inertia go, when the paper is pulled slowly? Does inertia depend on velocity? It is friction, acceleration and distance moved under this acceleration that have to be roped in for proper understanding.

The outcome of experiment depends on acceleration \(a_\mathrm{paper}\) of the paper (see figure). The forces acting on the glass are its weight \(mg\), normal reaction \(N\), and frictional force \(f\). Maximum value of frictional force is \(f_\mathrm{max}=\mu N=\mu mg\). By Newton's second law, acceleration of the glass is \(a_\mathrm{glass}=f/m\). If \(a_\mathrm{paper}\) is small then the paper and the glass moves together i.e., \(a_\mathrm{glass}=a_\mathrm{paper}\). Maximum value of \(a_\mathrm{paper}\) for the paper and the glass to move together is given by,

\begin{align} a_\mathrm{paper}=a_\mathrm{glass}=f_\mathrm{max}/m=\mu g. \nonumber \end{align}Beyond this limit, \(a_\mathrm{paper}>a_\mathrm{glass}=\mu g\) and hence the paper comes out leaving the glass on table.

## Note

This demo can be shown in multiple ways. Place a coin on the playing card kept above a glass. When playing card is pushed, the coin fall into the glass. Another variant is `Jiddi Sikka'. Fill a glass with sand. Insert a pencil in the sand with its flat end on the top. Place a coin on top of the pencil. Now ask a friend to throw the coin out of the glass without touching the coin or the glass i.e., only by hitting the pencil. Most likely, your friend will fail in the test.