Lab 5 : Modeling the fall of an object falling with air resistance

Part 1 : Determining the relationship between air resistance force and speed.

We have an expectation that air resistance force on a particular object depends on the object's speed, its shape, and the material it is moving through:
                                          F(resistance) = k * v^n 

First, we were going to the Design Technology building and do this lab by using video capture.

There is the linear portion of the position vs. time graph for 1 coffee filter falling from the balcony. we have a slope that means the acceleration = 1.049 m/s^2.

There is the linear portion of the position vs. time graph for 2 coffee filters falling from the balcony. we have a slope that means the acceleration = 1.219 m/s^2.

There is the linear portion of the position vs. time graph for 3 coffee filters falling from the balcony. we have a slope that means the acceleration = 1.686 m/s^2.


















There is the linear portion of the position vs. time graph for 4 coffee filters falling from the balcony. we have a slope that means the acceleration = 1.855 m/s^2.

There is the linear portion of the position vs. time graph for 5 coffee filters falling from the balcony. we have a slope that means the acceleration = 2.426 m/s^2.  

Then, plot all of accelerations and the mass of 1, 2, 3, 4, and 5 coffee filters to determine value for k and n.(like above two pictures)  And from this graph, we know the k = 0.01258, n = 1.497 .

Part 2 : Modeling  the fall of an object including air resistance.

We can use Excel to model the fall of an object with air resistance.








we start with the following conditions:

For my partner and I, we picked the mass of 3 coffee filters to test our measurements. we know the mass of 50 coffee filter = 46.3 g (for the mass of 1 coffee filter = 0.926 g).  after set up the k = 0.01258, m = 0.002778 kg(mass of 3 coffee filters), n = 1.497, gravity = 9.81 m/s^2, we choose the time interval △t= 0.01s.

From this data table, we could see that when t = 1.33s, the acceleration is almost equal to 0. for this moment, the velocity = 1.6759 m/s.    From the position vs. time graph for 3 coffee filters falling, we know the its velocity = 1.686 m/s.

Compare those two velocities, we could see that two velocities are so close which means our measurements are almost correct. And, the time interval 0.01s we chosen is the best to test the data.