PhysicsLAB Lab
Terminal Velocity

Purpose: The purpose of this lab was to find the relationship between an object’s terminal velocity and its mass. Terminal velocity occurs when the weight of the object (our coffee filters) exactly equals the upwardly directed air resistance. Air resistance depends on the object’s surface area and its velocity.
 
Equipment: Each group will need eight coffee filters, a stopwatch/phone to measure time, and a pre-measured distance.
 
Procedure: First, measure a reference height against an open wall that is greater than 1.5 meters above the ground. Record this height.
 
Refer to the following information for the next two questions.

Height measurements
Height to base of stairs = _____ meter 

Height of one stair = _____ meters 

Refer to the following information for the next eight questions.

We will begin by dropping one coffee filter from the second floor railing. This will provide enough distance for the coffee filter to reach its terminal velocity before it enters the pre-measured drop zone located between the bottom of the second-floor landing and the base of the stairs.  Begin timing the coffee filter when it reaches the reference height until it strikes the ground (stair step).  Repeat this for a total of three trials. Place your answers in the first data table below.

The coffee filter must be released bottom-side down. Moreover, you are not to give it any extra velocity upon release - just let it fall from rest.
 
 
     Trial #1 time _____________ Trial #2 time _____________ Trial #3 time ______________
 
     Trial #1 height _____________ Trial #2 height _____________ Trial #3 height ______________
 
Repeat this procedure with two, then three, then four ….. all the way up to eight filters. Place your rime and height data in the first data chart provided below.
 
Since terminal velocity is an example of constant velocity, you can then calculate the filter’s rate of fall by using the formula d = rt. Place your AVERAGE rate of fall for each set of filters in the second data table below.
 
number of filters Trial #1
time (sec)
Trial #1
height (m)
Trial #2
time (sec)
Trial #2
height (m)
Trial #3
time (sec)
Trial #3
height (m)
1 filter
2 filters
3 filters
4 filters
5 filters
6 filters
7 filters
8 filters
Refer to the following information for the next two questions.

Mass Measurements
 
When you return to the room, use a triple-beam balance to mass all eight filters so you can divide to get an average mass for one filter.
 
Mass of 8 filters = _____ grams 

Mass of one filter = _____ grams 

Refer to the following information for the next eight questions.

In this second data table, place your values for the mass of each set of filters and the AVERAGE velocity of each set of filters.
number of filters Mass
(grams)
Average Velocity
(m/sec)
1 filter
2 filters
3 filters
4 filters
5 filters
6 filters
7 filters
8 filters
Refer to the following information for the next nine questions.

Using EXCEL, graph two graphs: (1) the average terminal velocity vs mass of filters for all 8 sets and (2) the average terminal velocity squared vs mass for all 8 sets. Turn in printouts of your graphs.
What type of "trend line" did you use to fit the behavior of the data on the graph of average terminal velocity vs mass? 

What was the exponent on "x" for the graph of average terminal velocity vs mass? 

What was the slope of your trend line on the graph of average terminal velocity squared vs mass? (include units) 

The physics equation that models your data is FD = ½CrAv2 = mg. When you solve this equation for v2 you determine that the numerical slope of your trend line equals the expression (g/[½CrA]. Using C = 1.12, r = 1.225 kg/m3, and g = 9.8 m/sec2 you can solve for the area of the coffee filters. What is the value of your experimental area? 

The coffee filters have two possible candidates that can represent their area: just the flat bottom or the effective total area including the crinkled sides. The diameter of only the flat bottom was 8.5 cm while the cross-sectional diameter of the entire filter was 13.5 cm. If you use the larger of the two diameters what was the area of the filters. 

What was the percent error on your experimental value for the area? 

What was the y-intercept of your trend line? (include units) 

Where does your trend line best fit the data:


 
Elaborate on why you think your previous result occured.
 

Refer to the following information for the next two questions.

On the earth, a hammer and a feather are dropped from a tall balcony.
Which would hit the ground first? Why?
 

If they were released on the moon (which has gravity, but no atmosphere), which would hit the ground first? Why?
 

Refer to the following information for the next four questions.

What would you think would happen if one coffee filter had been wadded up and then released?
Would it take the same amount of time to reach the stair step? Explain.
 

Upon reaching terminal velocity, would the paper wad’s final air resistance be less, the same, or be greater than its final air resistance when it reached terminal velocity when not wadded up? Explain.
 

Would the paper wad’s terminal velocity be less, the same, or greater than its terminal velocity obtained in the experiment? Explain.
 

Would your previous three answers change if you instead wadded up 8 coffee filters? Elaborate.
 





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