12-Sept, 2016 . Lab #4: Modeling the fall of an object falling with air resistance

Lab #4: Modeling the fall of an object falling with air resistance

 Dahlia - Ariel - Carlos

12-Sept-2016

The purpose of the lab#4 is to help students know how to determine the relationship between air resistance force and speed.
Part 1: Collect data
We went to the building 13, and started to do the experience with dropping the coffee filters from a balcony.

Then, we used log pro to record data

We repeated drop 1,2,3,4,and 5 coffee filters at a time, thus, we had 5 videos in total.

Then we returned to class to analyze these video.

Part 2: Analyze 5 videos:

With log pro, we could record the relationship between the position of coffee filters vs time. Thus, with 5 video, we had 5 graphs.

* With 1 coffee filter:

* With 2 coffee filters:

* With 3 coffee filters:

* With 5 coffee filters:

* With 5 coffee filters:

To make them easier, I summarized them:

 Them I graphed them in log pro 

In which, x were the velocity of these coffee filters (the slope of period graphs)

                y were the force  (with 1 coffee filter, y=mg,

                                              with 2 coffee filters, y= 2mg, ....)

And because the mass of 150 coffee filters was 134.2 g; so the mass of 1 coffee filter was 0.8947 g.

and with g = 9.8m/s^2, I had graph:

This graph was the air resistance force.

Now, I had the equation of the air resistance force: F = 0.00373 v^1.929

Thus, 

The equation of acceleration, I got it from a free body diagram.

Part 3: Modeling the fall of an object including air resistance

Now, I opened a sheet of excel, and work the same way with the lab #3, the elephant problem

The interval of time was 0.01 s;
mass of 1 coffee filter was 0.0008947 kg;
gravity was 9.8m/s^2
k and n I got from the period part, part 2.
initial velocity was 0 m/s
initial time was 0s
in this sheet, time --------------------------A10=A9+$B$1
                     acceleration -----------------B9=($B$2*$B$3-$B$4*D8^$B$5)/$B$2
                     delta v------------------------C9=D9-D8
                     velocity ----------------------D9=B9*$B$1
Then, I filled them down until I had the constant velocity
*With 1 coffee filter:

Because delta t =0.01s was so small, and I had to filled down 315 rows to find the constant velocity, I changed the interval time into 1/30th. So, I had:
*With 1 coffee filter:

*With 2 coffee filters:

*With 3 coffee filters:

*With 4 coffee filters:

*With 5 coffee filters:

Now, I concluded that the bigger of the air resistance force, the larger of the speed we need.