25 Air Resistance
Name: _________________________________________
Date: _______________________
Partners:____________________________________________________________
Equipment
- LabPro Interface
- Motion detector
- Motion software file
- Large coffee filters
- Drag Excel file
Introduction
The motion of objects through air is studied in every introductory physics course. Ignoring the effects of air resistance, or drag, allows one to derive simple equations to predict the time of flight, range, and various other parameters of the motion. These equations are, however, only approximations to the true motions of real objects. Air drag is seldom so small that it can be ignored in the real world.
Unfortunately, the mathematics of including drag in the study of motion are quite complicated. However, by using an approximation scheme and the calculational power of Excel, you will develop a spreadsheet that can calculate motion parameters that are quite close to those measured in the real world.
I. Quantifying Drag
To quantitatively study the effect of drag on the motion of an object, we need to quantify what we mean by drag. Drag is a force that acts to oppose the motion of an object through a fluid. (To a physicist, air and water are both fluids.) This force depends on numerous parameters of the system.
Question: What parameters do you think drag depends on? (Imagine an object moving through air. What variables affect the size of the drag force?) Explain why each parameter affects the drag force.
Often, all of the parameters effecting drag except the speed of the object are lumped together into a single number, the drag coefficient. The dependence on speed will be determined in the following activity.
Place the motion detector on the floor and open the file Motion. Add a velocity graph to the display.
Hold a large coffee filter directly above the motion detector, as close to the ceiling as possible, press Collect, and release the filter. If necessary, repeat until you have clean data.
Question: Describe the motion of the coffee filter. Is the acceleration of the filter constant?
Question: Draw a free-body diagram for the coffee filter as it falls. Label the drag force Fdrag. Apply Newton’s Second Law in the vertical direction.
If the drag force was constant, both forces acting on the filter would be constant resulting in a constant acceleration. However, if the drag force depended on the speed of the filter, the drag force would grow in magnitude as the filter fell until the drag force equaled the weight of the filter. At this point, the two forces would be equal and the acceleration of the filter would drop to zero. The speed at which this occurs is termed the terminal velocity of the filter.
At terminal velocity, vT,
- If the drag force was proportional to speed, this would lead to:
and the terminal velocity would be proportional to the mass of the filter.
- If the drag force was proportional to the square of the speed, this would lead to:
and the squar