F(air resistance)= kv^n
Where v is the velocity an we are suppose to find K and N.
Apparatus: We used lagger pro to obtain all of our data. We used a special feature that captures pictures in time intervals of .1 seconds. This feature allowed us to find the coffee filters displacement at a given time. We would first record the drop of the filter rack and then use lagger pro to plot Blue dots of time and displacement as the picture below shows.
A picture of my lab Partners before our first drop.
After recording the drop we used the plot option in the video capture section to graph the drop of the filter after each time interval. As you can tell the displacement is getting longer as time moves forward. Eventually the displacement and velocity stays constant. When this happens, the filter has reached terminal velocity.
How we are going to obtain our data: We went to the Design Technology Building to capture all of our filter drops. We were asked to drop and record 5 different drops using video capture. The first drop would consist of one filter(About 1 gram). On the second drop, you would drop 2 filters.(About 2 gram) On the third drop, you would drop 3 filters(About 3 gram). On the fourth drop, you will drop four filters(About 4 gram). Finally on your fifth drop, you will drop 5 Filters(About 5 gram). The purpose of dropping and recording a different amount of filters is so that we could have data on the drop of 5 different masses. The Goal was to get these filters to reach terminal velocity one by one.
How we are going to use this data: Once we captured all of of video footage onto lagger pro, we returned back to our classroom where we recorded our data. We did exactly what the photo above demonstrates on all 5 of our drops. We plotted the blue dots which in return gave us a position vs. time graph. Our goal was to choose a section of the graph that would give us a linear fit. This linear fit will help us find our terminal velocity as well as our k and n values. Below are the photos of what the capture feature on logger pro recorded and plotted. The slope is equal to its Terminal Velocity.
One Filter:Terminal Velocity is Equal to -1.142m/s
Three Filter:Terminal Velocity is Equal to -2.065 m/s
Four Filter:Terminal Velocity is Equal to -2.156 m/s
Five Filter:Terminal Velocity is Equal to -2.894m/s
Using our data above we created a spreadsheet of the force and velocity of each drop
This is a picture of an objects mass and its terminal velocity
We then created a graph of Force vs. velocity. This graph had the section of 4 Filters struct in order to ge tumor accurate information.
4 Filters Struct
In order to be able to perform a power fit, we had to strike one of our data points to be able to come up with a model for our equation F(air resistance)= kv^n. Our graph is put in the form of F=av^b. The Graph gives us the Variables that we are looking for. a=.007563 and b= 1.764
Summary: We were able to record our drops using video capture and obtain the data needed to come up with our formula. The key to this Lab was to obtain the terminal velocity of each mass and plot it using a mass vs velocity graph. In order to get the information we needed we had to struck one of our points in order to insert a power fit. In doing so we came up with our formula.
F(air resistance)=.007563(v)^1.764
Now that we have obtained our formula we can now find the terminal velocity of an object depending on its mass or find the mass of an object depending on its terminal velocity.
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