March 11, 2015 Fall of an Object and Air Resistance Lab

Objective:
To find the relationship between the air resistance force and the speed of a falling object.

The Set-Up:

The photo of the balcony taken on the ground level

In Mt.SAC, building 13, the technology building, there is an indoor balcony. The advantage of indoor is that there is less unexpected force, such as wind, that could greatly affect our experiment. According to the instruction, some people stand on the balcony and drop the coffee filter. The way to drop the coffee filter is to hold it with two palms, and drop it gently, we want to make sure the coffee filter is stable while lowering.

Brown and white coffee filters

Our group choose the brown coffee filter to be the object because it is more visible than the white. We begin by lowering one coffee filter, we record by using video from the laptop, then we use loggerpro to help us analyze different points when the coffee filter is falling. We use a meter stick as a reference point for loggerpro. After we record the falling of one coffee filter, we add one more and did a recording with two coffee filters. We repeat the process until we have the video of five coffee filters falling.

Data Collection:

Velocity vs Time graph for 5 coffee filters

After recording five videos, we use loggerpro to analyze the videos. The results we get are five velocity vs time graph. The many dots on the graph represent different position of the coffee filter at different time. We choose the dots that are toward the end to analyze because they we are trying to find the terminal velocity and they are the ones that seems more consistent.  We use the linear fit option and get the slope of the graph; the slope is the terminal velocity.

Number of coffee filter (s)	Terminal Velocity (m/s)
1	0.9762
2	1.314
3	1.421
4	1.713
5	1.828

Next, we begin our calculation with an equation representing the air resistant force.

F= K * V^n

A few things to highlight of this equation:

·        ** The air resistant force (F) and v (terminal velocity) are proportional just like in the data table, the number of coffee filter is proportional to the terminal velocity

·         **The data from the table is a curved graph, it must involve some kind of exponent, therefore, in the equation v is to a power of n

·         **K represents a certain shape function

We can determine the values for k and n by plotting the data.

Distance and velocity graph

K=0.008846

n=2.678

Finally, we gather all the pieces of information and make a model according to Newton’s Second Law, F=ma.

Since this differential equation would be difficult to solve, we are going to use excel spreadsheet.

First we make eight columns and named them as t, delta v, v, a, delta x, and x. We set the time very small, such as 0.01 second so we can get a more accurate result.Under delta v, we input the formula, a1* delta t, because the acceleration times the change in time gives you the change in velocity. This change in velocity plus the initial velocity give you the final velocity, which is v. Next, gravity (9.8)- k/m* v^n gives us acceleration. The change in position is the average velocity times time. Lastly, final position is the sum of the initial positon and change in position.

Our goal is to look for a velocity when it becomes constant. This constant velocity is the terminal velocity of our experiment. 

Conclusion:

The excel that we use to derive the constant velocity

The terminal velocity is 1.842 m/s. This spreadsheet is calculated based on the mass of five coffee filters

Our experimental value of five coffee filters is 1.828 m/s, which is not far from our data!

The reason for this discrepancy might due to that fact that there is some other forces beside air resistance and gravity, such as when someone walks by or when someone opens the door, there could some random wind flowing around, which could affect the velocity. Other human caused errors could be the way we drop the coffee filter, though we try our best to keep it stable, the coffee filter could still fall on a random shape, which could influence the shape constant (K). Lastly, when we plot the point, we takes out a point, the velocity of three coffee filters, 1.421 m/s, because it is greatly out of the way. If we keep the third point, it could drastically change our result.

The graph with the third point that we taken out