The dependence of resistive force on the square of the speed is a model. Let\'s
ID: 2992450 • Letter: T
Question
The dependence of resistive force on the square of the speed is a model. Let's test the model for a specific situation. Imagine an experiment in which we drop a series of stacked coffee filters and measure their terminal speeds. The table presents typical terminal speed data from a real experiment using these coffee filters as they fall through the air. The time constant t is small, so a dropped filter quickly reaches terminal speed. Each filter has a mass of 1.64 g. When the filters are nested together, they stack in such a way that the front-facing surface area does not increase. Determine the relationship between the resistive force exerted by the air and the speed of the falling filters.
(a) Determine the proportionality constant from the graphs in the example.
b =
(b) What are the units of this constant when R is measured in N and v is measured in m/s?
kg/m
kg?m3/s4
N?m2/s2
kg?s2/m2
None of the above.
Explanation / Answer
a) Proportionality constant = y/x = 0.161/(3.22)2 = 0.015
b) Units = N/(m/s)2 = (kg-m/s2)/(m/s)2 = kg/m