Purpose: You will investigate how air friction causes terminal velocity using coffee filters. Part of this will include Interactive Physics computer simulations for multi-dimensional motion and air friction; this program is only on school computers.
Materials: Meter stick Stop watch and/or video Coffee Filters
For your report: You will need purpose; materials; data; and analysis sections for your write-up. It is always a good idea to organize data in tables so they are clear and neat, and include units on all measurements and results.
Keep in mind the BIG IDEA is that air friction (and friction in fluids in general) depends on how fast you move, fair = -kv, where k is a positive constant.
Read through each analysis part below carefully, because it will guide you through what we are looking for. Write things up using complete sentences. I recommend Google Docs for your report (just need a single report for the group).
Make some predictions prior to actually measuring the terminal speeds of the falling coffee filters.
Question: Does mass affect the terminal speed?
You can control the mass by using different numbers of filters.
Predict: What should happen to terminal speed as the mass increases?
Do it…make an appropriate data table with terminal velocity as a function of mass. Do several time trials and include standard deviations. Bonus: Determine the uncertainties on the terminal velocity results. You will need to do this using propagation of uncertainties as we have done in the past; see Above and Beyond below.
Do your best to estimate how long it takes for the filters to reach terminal velocity upon release. You’ll probably want to drop the filters from 2-3 meters high, so you get terminal velocities.
1. Determine the terminal speeds for at least five different masses of coffee filters. Estimate all measurement uncertainties and record those with your data.
Above and Beyond: This includes using the quadrature method for determining dv values for each terminal speed. Remember units are important on data and results.
dv = v [(dt / tavg)2 + (dd / d)2 ] ½
You and your partners need to come up with a reasonable estimate of uncertainty on the distance that the filters will fall; think of how well you can read the metersticks.
2. Use your measurements of terminal speed to determine values for k. Include these in a data table. What are the units of k?
3. Write concise conclusions of what your data suggest about the effect of mass on terminal speed. Make a graph in Excel of terminal speed as a function of mass (# filters) from your data. Use as large a range of mass as possible, up to a point where it does not have a measureable terminal speed (where it continues to accelerate before hitting the floor).
4. Sketch graphs (i.e. do not need numbers on the graph) of velocity as a function of time and acceleration as a function of time. Put graphs for different masses on the same set of axes so you can show a comparison of the effect of mass on terminal velocity and acceleration. Use different colors, or solid-dashed-dotted lines, to distinguish the different graphs.
5. Do a few trials for the other sized coffee filters, and draw any conclusions about how the size of coffee filters affect the terminal velocity. Explain/support your conclusions in terms of data and observations. Try to do this by holding mass constant between the filters as best you can.
6. For two of your small coffee filter examples, determine the percentage of kinetic energy that is lost due to air friction. Hint: think about how fast a filter should land if there is no air friction, and compare to your terminal speed at which it lands.
7. Log into your school account. Unfortunately, Interactive Physics is not online, only on school computers. Go to Programs, and go into the Science group of programs. You should find Interactive Physics. Go into IPFiles, and then Physics Experiments. In that folder find the Air Resistance folder. There should be 4 computer simulations, and run all four.
In each one, you can select different values of k. In some you can change mass, and in some you can change surface area. Run a series of controlled computer experiments for each simulation, and write summaries of observations/measurements and your conclusions about the effect of the various parameters on the trajectories of projectiles when varying air friction, terminal velocity, and so on.
Are these computer experiments consistent with what you see with the coffee filters? Explain.
The point of all this is to gain a good conceptual understanding of what air friction is all about, and gain a better understanding of the complexity of reality, as opposed to the ‘physics land’ we tend to visit in most problems. Still, keep in mind that we are using a highly simplified model for air friction, and reality is still quite a bit more complex than we are treating air friction for things like cars, planes and rockets moving through the atmosphere (aerodynamics). Aerospace engineers need to deal with the complexities in a major way. J