The radius of a growing soap bubble is measured against time after it starts forming

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Quantities, units and the practice of measurement · Data analysis and model fitting in the laboratory

Measurement and Method, Ch What dimensions decide before you measure anything

Problem

The radius

R

of a growing soap bubble is measured against time

t

after it starts forming, and plotted on log-log axes. Four points read off the printed graph are: Data:

t=1,\ 10,\ 100,\ 1000\ \mathrm{ms}

with

R=2.0,\ 6.3,\ 20,\ 63\ \mathrm{mm}

respectively. ((a)) Read the slope of the straight line these points define on log-log axes. ((b)) Write the scaling law connecting

R

and

t

, including a numerical value for the constant of proportionality with its unit, using the

t=1\,\mathrm{ms}

point to fix it.

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