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labs_251 [2019/08/15 14:10]
river removed
labs_251 [2019/08/28 11:01]
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-====== Free Fall (Wikilab Test======+Throughout the semester, students will be explore classic physical systems as a tool to increase their overall laboratory skills ​(i.e., experimental design, data analysis, collaboration,​ and scientific communication). In this course, students will be guided and supported through their development of these practices by emphasizing\\ 
 +  -How to carry out experiments effectively by collecting data while attempting to minimize uncertainty.\\ 
 +  -How to connect the results obtained experimentally with theoretical models in lecture while recognizing the limitations of each.\\ 
 +  -How to thoroughly document the experimental design, data collection and analysis, the results, and the discussion/​conclusions.\\ 
 +  -How to report and communicate findings obtained in the laboratory.
  
-===== Purpose =====+[[Free Fall]]
  
-We have all learned that gravity pulls on things at the same rate. +[[Inelastic Collisions]]
-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 +[[Energy Transfer]]
-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 =====+[[Impulse]]
  
-In order to investigate the effects of air resistance on an object'​s +[[Pendulum]]
-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?+
  • labs_251.txt
  • Last modified: 2019/08/28 11:08
  • by river