Quantitative presentation example:

Does a paper ball and scotch tape pendulum behave like an ideal pendulum?

Arnando ShastriniMinnesota State University

Moorhead

Introduction

• Laws of pendulum motion first developed by Galileo

• In textbooks a pendulum is idealized as a point mass on a massless string L. In the absence of air resistance and for small angles

• Would a pendulum made of scotch tape and a wadded sheet of 8.5X11 inch paper follow this law? Would air resistance be substantial?

Experiment •One sheet of 8.5X11 inch typing paper was crumpled into a loose ball approximately 2 inches in diameter.•A piece of scotch tape 2 cm wide was attached to the paper ball.•The tape was attached to a door frame.•The distance L was changed, and the period T measured.

L Tape

Paper ball

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.20.40.60.8

11.21.41.61.8

2

f(x) = 4.12818560747088 x

Period squared versus pendulum length

Series1Linear (Series1)Linear (Series1)

Pendulum length (m)

Perio

d sq

uare

d (s

^2)

Results

Discussion

• For an ideal pendulum, one expects the slope of T^2 versus L to be =4.0 s^2/m

• In this experiment, the slope was 4.1 s^2/m• The relationship between L^2 and T seems to

follow the behavior for an ideal pendulum in the range of L selected.

• The theoretical and experimental values are in good agreement, though formal error analysis was not performed.

Conclusions

• It appears that a pendulum made of a paper ball and scotch tape follows the behavior of an ideal pendulum very well within the range of pendulum lengths studied.

• Air resistance is expected to affect the longer periods more, because the longer length of tape is expected to cause more drag.