Lab 6 Drag Force on Coffee Filters

In this lab we will try and study the relationship between drag force and a falling body.

 To conduct this lab we needer a computer with the Logger Pro software, Lab Pro, motion detector, nine coffee filters, and a meter stick.

We are told that the force of drag increases with the velocity of an object. We will start by assuming the drag force, F(d), has a simple power law dependence on the speed given by

                                F(d) = k |v|^2 where the power n is to be determined by the experiment

Because the filters have large surface area and low mass, they will reach terminal speed soon after being released.

So to start the experiment we take 9 coffee filters and release them about 1.5 meters above the sensor and let it record the position vs time.

Then we use a Linear/Curve fit on the part of graph where it has reached terminal velocity to determine its value.

We average five readings of each trial. We then take one trial for eight coffee filters, one for seven coffee filters, and so on, all the way down to one coffee filter.

In Graphical Analysis, we made two columns for a data table. The first column was the packet weight (number of filters) and the average terminal speed (|v|) in the other. The packet weight was the y-axis vs terminal speed (not velocity) in the x-axis. Perform a power law fit of data and record the power, n, given by the computer. Then figure out the precen error.

Our (n) value was 2.21 and our precent error was 10.5%

Finally we had to take our equation F(d) = k |v|^n and compare it to what the books formula of drag.

our equation :       F(d) = 1.39 (|v|)^2.21

book equation :    F(d) = .25A(|v|)^2

We came within 10% of the actual value. The fit parameter represent the surface area of the coffee filter, in this case it was proportional to the weight and number of filters.

The first question asked by the lab was why is it important for the shape of the coffee filter to stay the same? Since the force of drag is proportional to the surface area, it is very important that the surface area is not decreased or else force of drag would decrease and the terminal velocity of the coffee filter will increase. 

The second question asked by the lab was what should the position vs time graph look like. Well since the object is accelerating because of gravity, it will start with a concave down graph, until it reaches terminal velocity then it will have a straight line. Both parts will be negative because the coffee filters are going downward. The third question asked what should the slipe of the curve fit represent? As we stated earlier the slope represents the terminal velocity, because it is a straight line, that means acceleration is zero so the velocity is not changing. The major source of error could have come from pinching the coffee filters and making small dents in the surface area. Other places we could have found error was particles in the air or interference with the path of the radar. Also we could have error in selecting the area of curve fit.

 

Lab 2 Acceleration of Gravity

The purpose of this lab was to determine the acceleration of graity for a freely falling object and to gain familiarity with the computer as a data collector.

The equipments needed for this lab were a Lab Pro interface, Logger Pro software, Windows computer, motion detector, rubber ball, and wire basket.

The first step was to connect the motion detector to the Lab Pro interface and load up the Logger Pro software on the computer. The computer started with a blank graph of position verse time. From that graph it could also calculate the velocity versus time at any instant.

Next we placed the motion detector on the floor facing upward and a wire basket over the motion detector for protection.

Now we're ready to collect data. Gently toss the ball straight up from a point about 1 meter above the detector and do so that the ball goes straight up and down. This will equate into a parabolic graph.

Once you get a nice parabolic graph of position vs time click on the Analyze/Curve fit and fit a quadratic line fit. For the velocity vs time graph choose a linear fit. The quadratic fit will give you three coeffecients for your graph, a*t^2+b*t+C, with doubling the first (a) and you will get acceleration of gravity. The linear fit will give you an m*x+b fit where m is the value of gravity. 

Take five good trials and record their values for (a) and (m) then calculate the % difference from the actual value of gravity 9.81 m/s^2. To find percent error you use the following calculation

                                   Percent error = (Measured - actual)/actual * 100%

Trial	G(2a) (m/s^2	% error	G(m) (m/s^2)	% error
1	9.658	1.5	9.776	0.34
2	9.228	5.9	9.145	6.8
3	9.76	0.51	9.68	1.3
4	9.686	1.3	9.57	2.3
5	9.282	5.4	9.611	2

In conclusion I was at first confused as to why we multiplied the front value of the quadratic fit by 2 in order to get the value of gravity, but then remembered that the kenimatic equation for position versus time is X=X+Vt+1/2At^2. Which means gravity is multiplied by 1/2, hence the quadratic fit was expressing 1/2 the acceleration which makes complete sence. Then the lab asks why should your graph be a nice parabolic shape. The reason is because gravity, the second derivitave of position verse time, is constant at -9.81 m/s^2 meaning that the graph is concave down and that velocity is contantly decreasing. Then the lab asks why does the curve of velocity vs time graph have a negative slope, and what does the slope of the graph represent? The negative indicated the direction in which the velocity is changing, and in this case the motion sensor chose down as a negative direction, hence the slope, also gravity, was a negative value. Going back to the second question, what does the slope represent; it is the value of gravity, because acceleration is the slope of velocity. Finally coming to errors, there seemed to be errors, mainly to how well the ball was tossed up and down and whether it was straight up and down or whether it was projected at an angle. Also particles and drag could affect the resuls, drag more so.