Terminal Velocity of a Coffee Filter#
In one of the PHYS 111 labs Mateo measured the terminal velocity \(v_T\) of a coffee filter of mass \(m\) falling through the air. In equilibrium, the drag force acting on the coffee filter exactly balances the gravitational force on the filter such that:
\(bv_T = mg\)
where \(b\) is a “drag coefficient” determined by the shape of the filter and the density of the air.
Suppose that the following six measurements of a coffee filter’s terminal velocity were made:
Trial |
\(v_T\) (\(m/s\)) |
|---|---|
1 |
0.93 |
2 |
0.96 |
3 |
0.92 |
4 |
0.84 |
5 |
0.89 |
6 |
0.83 |
The standard deviation of this data set is 0.047 \(m/s\).
Part 1#
Use the experimental data to determine the uncertainty in the average value of the terminal velocity. State your answer using the appropriate number of significant figures.
Answer Section#
Please enter in a numeric value in \(m/s\).
Part 2#
Use the experimental data to determine the average value of the terminal velocity. State your answer using the appropriate number of significant figures.
Answer Section#
Please enter in a numeric value in \(m/s\).
Part 3#
If the coffee filter has a mass of \(m = \) 3 \(\pm\) \(g\), determine the value of the uncertainty in the drag coefficient \(b\). State your answer using the appropriate number of significant figures. Assume that \(g= 9.81 kg/s\) and has negligible uncertainty.
Answer Section#
Please enter in a numeric value in \(kg/s\).
Part 4#
If the coffee filter has a mass of \(m = \) 3 \(\pm\) \(g\), determine the value of the drag coefficient \(b\). State your answer using the appropriate number of significant figures. Assume that \(g= 9.81 kg/s\) and has negligible uncertainty.
Answer Section#
Please enter in a numeric value in \(kg/s\).
Attribution#
Problem is licensed under the CC-BY-NC-SA 4.0 license.
