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+====== Free Fall ======
+===== Purpose =====
+We have all learned that gravity pulls on things at the same rate.
+Therefore, a bowling ball and a feather will experience the same
+gravitational acceleration. Seemingly in contradiction, you
+instinctively know that if you dropped a feather and bowling ball at the
+same time, the bowling ball would land first. Despite being often
+ignored in lecture, air resistance is an aspect that can't be ignored in
+practice. In fact, it is an important consideration when exploring how
+objects move in our world, something no skydiver would contradict.
+In this lab, your group is tasked with observing how objects fall and
+the ways air resistance affects them. By investigating the concept of
+terminal velocity, you will model how an object's maximum speed is
+related to its mass. Along the way, you should become more familiar with
+the equipment and data analysis techniques you will be using throughout
+the semester as well as developing productive skills to work more
+effectively in groups.
+===== Theory =====
+In order to investigate the effects of air resistance on an object's
+trajectory, it is important to review some important principles. We know
+that the force acting on an object can be rewritten as a sum of all
+other forces on it. This is an experimental fact, something we observe
+time and again in many different experiments. That is,
+$${\overrightarrow{F}}_{\text{Net}} = \Sigma{\overrightarrow{F}}_{i} = {\overrightarrow{F}}_{1} + {\overrightarrow{F}}_{2} + \ldots$$
+where${\overrightarrow{\ F}}_{\text{Net}}$ is the total force on an
+object and ${\overrightarrow{F}}_{i}$is the individual contribution of
+each force. It is important to remember that these forces are //vectors//,
+and therefore the direction of each force matters.
+From Newton's second law, we know that the acceleration of an object
+(//a//) is relative to the mass of that object (//m//) and force acting on
+it (//F//). Again, this result comes from many experimental observations
+of objects experiences forces. More commonly, we see this written as
+$$F = \text{ma}$$
+When considering freely-falling objects, the acceleration that they
+experience is //g//.
+Air resistance, another force acting on a falling object, can be
+considered as
+$$F_{D} = \frac{1}{2}\rho v^{2}C_{D}A$$
+where
+  * $F_D$ is the drag force
+  * $\rho$ is the mass density of the fluid
+  * $v^2$ is the velocity of the object
+  * $C_D$ is the drag coefficient
+  * $A$ is the area.
+By combining these equations, we can determine the acceleration each
+object feels as well as the terminal velocity of an object, dependent on
+its mass. Take note that the gravitational force and the drag force act
+in diametrically opposed directions for objects falling in a straight
+line.
+===== Research Concepts =====
+In this lab, like many others this semester, you'll likely benefit from
+video tracking and obtaining your data from the videos. As such, prior
+to class it's useful to understand:
+  * What terminal velocity means and what parameters on which it depends
+  * What a vector means and how they can be combined
+  * How the above equations can be combined to determine the relationship between mass and terminal velocity
+  * How you can determine the speed of an object from a displacement vs time and velocity vs time graph.
+Additionally, you will be using video tracking software in many labs
+this semester, including this one. Therefore, it would be useful to:
+  * Download video tracking software from [[http://physlets.org/tracker/]] (the computers in the lab have this as well, but it may be useful on your own devices, too)
+  * Understand how to use the software, especially regarding how to track specific objects and how to analyze data ([[http://physlets.org/tracker/help/frameset.html]])
+  * Look up the frame rate of the camera in your phone, as well as what slow-motion options it has (and the frame rate for any slow motion functions on your phone).
+===== Tracker Tips =====
+Throughout the semester, you will be expected to make decisions with
+your data and apparatus when conducting experiments. However, because
+this is the first time you will be using the video tracking software, we
+wanted to share some tips to help expedite your data acquisition and
+analysis. This list is not exhaustive, and complications in an
+experiment can arise unexpectedly. However, these common issues can be
+avoided through thoughtful experimental design:
+  * Pay attention to your surroundings, ensuring that there is enough contrast between the falling object and background, especially if the background is in focus.
+  * Many videos will look the same, so finding a way to designate between them will expedite analysis.
+  * Consider a way to calibrate parameters on the video, especially distance.
+  * Ensure your camera is being held still
+  *  Try taking and analyzing a test video before taking all of your data. You may determine some issues with your setup that you can fix before it's too late.
+===== Free Fall Experiment =====
+**Part 1 -- Determining "g" from a Free-Falling Object**
+You all know that letting go of a carried object will cause it to fall
+due to gravity. However, using video-tracking software, we can obtain a
+value for the acceleration of the fall, or "g." With your group, choose
+an object to drop, recording the fall with a camera (i.e., your phone).
+//You are responsible for your equipment, so make sure the object you
+choose will not break.//
+Obtaining valuable data will require participation from the entire
+group. There are many aspects to consider while conducting this
+experiment, so determine with your group who will be responsible for
+each aspect in order to conduct your experiment efficiently. When
+recording this free-fall, consider:
+  * The equation you are using to model the object's motion
+  *  What parameters you will need to know or measure (i.e., distance, time, mass, etc.) and how you will be obtaining them from the video or the data?
+  * What sources of uncertainty you are considering and the relative effect of these sources?
+From your video data, determine the acceleration of the object.
+  * How does it relate to the "known" value of g, 9.81 m/s^2^?
+  * Can you account for any differences between your value and the "known" value?
+**Part 2 -- Observing Drag **
+You just observed what happens when dropping a bulky object, but as you
+know intuitively, a bowling ball and a feather don't fall at the same
+rate. Therefore, an object's properties must be a factor determining how
+fast it falls. We can observe this by tracking an object we know will
+fall differently, like a coffee filter.
+Drop a coffee filter from an appreciable height and watch how it falls.
+When making observations of the falling filter, consider:
+  * How does the filter fall? Why is this so different from the object dropped in **Part 1**?
+  * Does the way the filter fall depend on how it is dropped? Consider dropping the filter with different orientations to draw conclusions.
+  * Are there ways you can design your experiment to maintain consistent orientation during the fall?
+  * Is there a minimum height you can drop the filter from to make sure it reaches terminal velocity?
+**Part 3a -- Determining Terminal Velocity **
+When you are ready to take quantitative data, record the motion of the
+filter as it falls, using the video tracking software to help analyze
+your data. How you determine the terminal velocity from your video will
+be up to you and your group, but keep in mind your variables and the
+benefits of the tracking software, such as the graph and data tables.
+(Keeping these in mind will help with the rest of the experiment.) While
+analyzing your data, it would be useful to consider:
+  * How are you determining and measuring the terminal velocity?
+  * How confident are you that the filter has reached terminal velocity?
+  * How can you use your data to help increase confidence in the value reported as well as decrease the uncertainty?
+  * What might happen to the terminal velocity if you stack multiple coffee filters?
+**Part 3b -- Determining the Relationship Between Mass and Terminal
+Velocity**
+By stacking filters, you can change the mass of the object without
+adjusting the shape (i.e., your drag coefficient and area remain
+constant). That way, you can investigate how the terminal velocity is
+related to the mass of the object without changing any of the other
+variables in your equations.
+  * While adding coffee filters, is there a point at which terminal velocity is no longer observable?
+  * If so, can you adjust your experiment in order to still measure this? Think of all the variables in the equation and in your experiment (i.e., those not necessarily in the equations).
+  * If you can no longer determine terminal velocity, why not?
+  * How many different masses are you able to test before you can no longer determine terminal velocity?
+**Part 4 -- Synthesizing Your Data**
+You can determine the terminal velocity of each individual video using
+the tracking software. In order to relate each trial, you will have to
+use Excel (or similar software). Transfer your data into Excel and
+determine how terminal velocity depends on mass. When modeling data, it
+is often helpful to represent the data graphically. When creating your
+graph, consider:
+  * Under what parameters does your plot become linear?
+  * How does this relate to the theoretical equations given? Does your data support theoretical models? Why or why not?
+  * If so, can you determine any quantitative information from your plot? (When modeling, the slope and intercept are often useful values.)
+  * If not, why not? What factors make the relationship difficult to determine?
+  * Are you able to conclusively determine anything from your data? If not, what would you need to be able to draw conclusions?
+===== Questions to Think About =====
+As you conduct your experiment, it may be helpful to consider:
+  * How are you assigning your uncertainty?
+  * Are there ways to design your experiment so that you minimize your uncertainty?
+  * What is your goal for each part? Have you considered how you will analyze your data, ensuring your design will be appropriate?
+  * How are you going to determine when the filter moves at terminal velocity?