free_fall

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free_fall [2019/08/15 14:12] (current)
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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?
  • free_fall.txt
  • Last modified: 2019/08/15 14:12
  • by river