Thursday, October 20, 2011

Lab #6 Air Resistance

Introduction:

In previous labs, we neglected air resistance and found the velocity of falling objects. Now we are going to show how air resistance affects the velocity of a falling object. Air resistance can be found by following:





A is the cross sectional area, C is the drag coefficient, and ρ is the density of air.


We can say that when a falling object is at terminal velocity, then Fair = mg.


Overview:

In this lab, we are dropping coffee filters from a certain height to model air resistance on an object. We chose to use coffee filters because we can stack multiple coffee filters on top of each other so that only the mass will change in our equations. The term ρAC will remain constant throughout the whole experiment. Our goal in this experiment is to show how mass affects the terminal velocity.

Materials:

* 5 of the same coffee filter
* LoggerPro
*Velocity/Position Detector

Procedure:

1) Record initial height
2) Drop coffee filter(s)
3) Record the slope near the end of the position vs time graph of the fall (this is our terminal velocity)
4) Record the time of the fall
5) Repeat steps 1-4 about 5 times to obtain a range of data
6) Repeat steps 1-5 for 1,2,3,4,5 coffee filters
7) Record mass of one coffee filter (assume all 5 coffee filters are the same mass)


Data: (Here is a showcase of my awesome HTML skills)

mass of a coffee filter = .00103kg
ρAC is a constant

Here is the data we collected for all filters:

1 Coffee Filter

Terminal
Velocity     Height    Time
.8616m/s 1.298m 1.67s
.6668m/s 1.261m 1.85s
.7242m/s 1.2m 1.65s
.8318m/s 1.208m 1.6s
.7069m/s 1.191m 1.6s
    .084        .046     .105  --  Deviation

2 Coffee Filters

Terminal
Velocity    Height  Time
1.122m/s 1.248m 1.2s
1.036m/s 1.228m 1.2s
1.183m/s 1.218m 1.2s
1.127m/s 1.256m 1.3s
1.204m/s 1.241m 1.25s
    .065        .015     .045  --  Deviation

3 Coffee Filters


Terminal
Velocity    Height  Time
1.49m/s 1.225m .1.05s
1.277m/s 1.216m 1.05s
1.581m/s 1.187m .95s
1.505m/s 1.223m 1s
1.361m/s 1.239m 1.05s
    .122        .019     .045  --  Deviation

4 Coffee Filters


Terminal
Velocity    Height  Time
1.81m/s 1.19m .85s
1.87m/s 1.229m .9s
1.762m/s 1.195m .85s
1.824m/s 1.107m .8s
1.861m/s 1.174m .8s
    .043        .045     .042  --  Deviation

5 Coffee Filters


Terminal
Velocity    Height  Time
1.988m/s 1.144m ..75s
1.88m/s 1.146m ..7s
1.943m/s 1.235m ..9s
2.02m/s 1.068m .7s
1.963m/s .998m .65s
    .052        .09     .096  --  Deviation

Analysis:


The data is a little messy. We didn't drop from one specific height (even thought we should have). As we can see from our data, as we add more filters the velocity increases. We can compare this to our model:
Fair = .5ρACv^2    and
Fair = mg, so


.5ρACv^2 = mg, and from this model we can calculate velocity


v =  , and from this we can see as the mass increases the velocity will increase and
                        our model agrees with our data

1 comment:

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