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.
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
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.
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:
Additionally, you will be using video tracking software in many labs this semester, including this one. Therefore, it would be useful to:
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:
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:
From your video data, determine the acceleration of the object.
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:
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:
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.
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:
As you conduct your experiment, it may be helpful to consider: