In most physics problems we make certain assumptions. Sometimes these are justified, other times they are not. This week we will look at the effects of drag.
The free-fall model assumes that when we drop an object the only force acting upon it is its own weight, and hence the object will accelerate downwards at the familiar 9.8 m/s2. In reality, the object will have to push air out of its path, and by Newton's Third Law, since it is pushing down on the air, the air below is pushing back upwards on the object. From a simplistic point of view, the faster an object is falling the more air it will have to push out of the way, and hence the greater upwards force it will experience.
There are two models for this force, called the drag force. In some cases the drag force is linear with the velocity of the falling object (FD = -b v), in others it is proportional to the square of the velocity (FD = -b v2). In either case, the drag force will oppose the direction of motion, so for an object that is dropping straight down the drag force will be opposite the weight. If an object is going fast enough, the drag force will balance out the weight, and the object will stop accelerating, and will this have a constant velocity (mathematically this isn't strictly true, the object's velocity will asymptotically approach this velocity). This is known as the terminal velocity.
In today's lab we'll use motion detectors and coffee filters. Set up your motion detector so that it is over the floor rather than over the table. Collect position data while dropping one single coffee filter. Determine the terminal velocity from the motion detector data. Repeat with a pair of filters stuck together, and continue to take data until you've dropped a mass consisting of seven or eight coffee filters.
Graph your terminal velocity and mass data. Think carefully about how to do this in a way that
is the most revealing. In your conclusion describe what that tells you about
air drag on coffee filters.
Drag Forces - Pre Lab Activity
In lab this week we will look at dropped coffee filters and measure the terminal velocity as a function of mass. To do this you will collect position vs. time data, and then manipulate this in Excel. In order to give you practice, we've written an Excel spreadsheet that generates fake position vs. time data. Download the spreadsheet and enter the month and day of your birth into the first two cells (the default values are 6 and 15). From your graph of position as a function of time determine the terminal velocity for 1,3,5 and 7 filters worth of mass. Show that one of the columns of data uses linear drag, and the other uses quadratic drag. To keep things straight, we use Mars gravity in this simulation.