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

Air Resistance

Samuel
Ellis
Mia
9-19-2016

2. 

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. We can model this expectation as a power law. 

3.

Power law = F_resistance = kv^n. k is constant(shape of object density of air), v is speed. To determine a falling object, we need to know it speed and exponent and base on those data we can find air resistance. 

4.

  1. Turn on LoggerPro, open "video capture" 

  2. Capture video for 1,2,3,4, and 5 coffee filter falling from balcony.

  3. Get terminal velocities for each one by fitting the linear portion of the position vs time graph for each.

  4. Plot your data appropriately to determine values for k and n. 

  5. In excel worksheet, label t, a, delta v, and v.
  6. Set t = 1/30 of a second
  7. Once you have calculate columns in excel for v and x as function of times, determine what your model predicts for the terminal velocity of the various coffee filter. 

  

5. 

150 coffee filters = 134.2g

1 coffee filter = 0.895g

Slope

1= 1.537

2=   2.28

3=   2.74

4=   3.33

5=    4.10

A= 0.00419+- 0.005

B= 1.777+- 0.1179

6.

 (Then we input different mass of coffee filter to get air resistance force)

(Find in what time does velocity stop increasing) 

7.

  

Above, is the speed vs air force graph. We inputted the speed of coffee filter(s) from 5 different weights along with their air-resistance force. And then used "power fit" curve to find the equation of the curve, which turn out to be k= 0.00419+- 0.0005 and n= 1.777+-0.1139. 

8.

At the end, we generate an equation for air-resistance force acting on coffee filter. Air-resistance force increase as velocity increase. We first determine filters speed by video taping it falling speed, then used 1 meter ruler in the video for reference distance so we can plot point as every 1/30 of a second. So we find our speed and time, we just need to use power fit to find its equation.