Kevin Tran
Lab Partners: Kevin Nguyen, Jose Rodriguez
March 17, 2017

Modeling the fall of an object falling with air resistance

Purpose: Determine the relationship between air resistance force and speed.

Introduction: My partners and I went to the Design Technology building to video capture our teacher dropping coffee filters with different masses. He will be dropping coffee filters with 1 stacks, 2 stacks, 3 stacks, 4 stacks, and 5 stacks. We will record 5 different drops as the coffee filter drops down due to gravity and air resistance pulling the object in the opposite direction to slow the object down. In theory, if the object is heavier, the velocity will increase and so will the air resistance.

The formula for air resistance is F=kv^n 

F=Air resistance

k= shape and area of the object

v= velocity

n= trials

The location where the lab occurred. (picture below). Our teacher dropped the 5 different masses during this experiment.




Now, I will display all the position time graph in the order of coffee filters (1-5) with air resistance. Let's first note that each coffee filter is 0.878g +/- 0.02g

Coffee Filter 1 stack:

Coffee Filter 2 stacks:



Coffee Filter 3 Stacks:



Coffee Filter 4 stacks:

Coffee Filter 5 stacks:



These 5 graphs represent the position( x and y included) and time graph.

In order to find the values for k (The shape and area of the object) and n (trials) , we have to create a weight and velocity graph with all the 5 different coffee filter weights. (picture below).

Below, we created a weight and terminal velocity graph in order to find the k and n values.


k in this case would be "A:". Where k is 0.003054N(s/m) +/- 0.001011 N(s/m)
n in this case would be "B:". Where n is 2.555 +/- 0.3504


Now, I will be displaying the numerical results of each of the 5 weights in their corresponding order.

Coffee Filter 1 stacks:



Coffee Filter 2 stacks:

Coffee Filter 3 stacks:


























Coffee Filter 4 stacks:



Coffee Filter 5 stacks:



























Note: The yellow mark represents its terminal velocity.

In the 5 graphs we have the variables: delta t (seconds), mass (kg), gravity (m/s^2), k (N*s/m), and n.

With this information and the position/time graph, we are able to find each of the variables: time(seconds), velocity(m/s), net force(N), Acceleration(m/s^2), delta v, average velocity, and delta x.

This model works because we are given all the approximate results of all the variables that we acquire to determine how much air resistance can affect velocity as it is moving.

In order to derive k and n, we do the following (work below).



Now, we will find the uncertainty of the coffee filter.

For the weight of the coffee filter, we have an relative uncertainty of 2.28% ((0.02g / 0.878g) x 100) and a relative error of -2.22%((0.878g -0.898g)/ 0.898g x 100)

Conclusion: The lab has taught us how effective air resistance is to the velocity of a moving object. Our theory was correct, the faster the object moves, the more air resistance will push against the object. In addition, the heavier the object, the faster the object will go, which will lead to more air resistance going against it.