Modeling fall of an object falling with air resistance

Purpose: The purpose of this lab is to determine the relationship between the air resistance force and speed of an object. We expect there to be determining factors in the the force resistance and graphs to show us relations.

Process: 

1)We studied this relation of air resistance and speed by using coffee filters as our objects that would drop from a second story balcony in a building. We found there to be factors in determining the air resistance force. These factors are generally the objects shape and speed. This equation is found to be  force of air resistance =kv^n. The k in this formula relates to the shape and area of the object. 

2) We used the video capture to capture 5 coffee filters dropping from the second balcony. We expect to find that each of these coffee filters reach terminal velocity eventually as they fall.  We then took the graphs that were recorded and attempted to linearize the curve we could obtain the terminal velocity. The slope is key to finding a velocity from the position versus time graph.

3) The next step was to take our data and then in excel create a table that would provide us with the terminal velocity. We created a table with columns. The time, change in velocity, velocity, acceleration, change in position, and position columns would eventually give us terminal velocity. We also added space for the k and n values of our equation. Smaller and smaller increments of time would give us a better result for our terminal velocity.

Conclusion: From the equipment we used and considering that excel is a good programming for acquiring this kind of data we our confident that our results are a good representation of terminal velocity.

Free Fall and Experiment Uncertainty

Purpose:
The purpose of this lab is to determine and examine the value of gravity when all other external forces are absent. We expect to find this value of acceleration to be 9.81, as the object is in free fall.

Process:
1)To perform this experiment we must set this apparatus up that will mark the falling object as it falls to the ground. The tape attached to the apparatus will mark the distance of the object as it falls in intervals that will give us two graphs. These two graphs are the position vs time graph and acceleration vs time graph, which will be able to allow the calculation of acceleration.There will be a series of dots on the paper that will correspond to the position of the mass as it falls for every 1/60th of a second.

2) We must then place a ruler next to the apparatus and line it up next to the tape, lining the two-meter stick with the 0-cm mark with the highest dot. We will record the position of the object as it falls through each dot respectively.

3) Open Microsoft Excel and then we will enter the data we took and also label our columns as Time, Distance, the change in distance and the change in time and the speed. From our data we will create a graph that will give us these graphs of distance and speed that we desire.

Analysis:
The uncertainty that we can find in our calculations can come from a misreading of the measurements from the tape, or even by our miscalculations of calculating data on excel . The graphs of position and velocity with respect to time can give us the acceleration due to gravity. In order to get the acceleration of these graphs, we must look at the slope of the graphs at a certain point or points. The slope will give us either a tangential value if specifically the slope at one point or the average value at two points. We expect to also find uncertainty to occur because nothing is ideally perfect, but the instruments we are using are expensive and the most accurate tools we can use. Two ways we can express this error is the absolute difference in our calculations, which is the result for acceleration that we got minus the actual acceleration that it is, or relative difference, where we take the value we got minus the actual divided by the actual multiplied 100, which will give us our percentage.

Conclusion:
The experiment led us to be able to use excel and calculate acceleration, along with plotting graphs and also being able to analyze data from graphs to obtain acceleration and realize nothing is ideal and prone to mistake. To make less mistakes is to replicate the experiment multiple times, which will give us a more stable answer.

3-March-2015: Finding a relationship between mass and period for inertial balance

Purpose:
The purpose of this lab is to find the relationship between a mass and its period using an inertial balance, which involves a power law equation that will show us the relation mathematically. We see how different masses and their respective periods behave on this device.

Process:
The inertial balance seen in the upper right hand of the paper, which will allow us to put masses on top of it and give us oscillations and a period of the mass.

The data that we took first was placing masses on top of the inertial balance. W started with 100 g, then proceeded to add more as we took the result for the period of each mass corresponding. We did this until we reached 800 grams, seeing 8 different results for the period and seeing a definite pattern. The period would increase as more mass was added to the inertial balance, which we then apply a force and see the resulting oscillations which we then cut off at a certain point to get the period. We also included two unknown masses.

We then proceeded to plot the equation T=A(m+Mtray) to the n power by taking the natural logarithm of each side and getting an equation very similar to the line equation y=mx+b. We must obtain the values of A, which is a constant, Mass of the tray and the exponent n.  The graph would not be perfectly straight line, but to obtain Mtray we would need to try different values until we obtain a relative straight line. Then linear fitting it would give us the straight line we were looking for as shown above.
 Conclusion: 
Overall we plotted data with varying mass values, obtained the periods of each mass and saw that plotting the power law equation with the right values of Mtray gives us the desired line.