STEM – Floating Through Air (Mini-Math Lesson – Algebra 2)

This weeks final STEM activity is also a relatively easy one for students to do on their own. And it is a lot more exciting and realistic to collect your own data and analyze the results than to just use given data. Makes the math more ‘real’. However – as with all the activities this week, there is provided sample data.

Today’s activity has to do with falling objects and how gravity and area have an impact on the resistance and acceleration of that object as it falls. Materials needed are pretty basic – a book of some sort and a piece of paper, measuring tape on a vertical wall, and either a stop watch or a camera (video) to record the fall of the object when dropped from a 6 foot height. Video probably works best because you can slow it down and look at the height frame by frame.  At least two people would work best.

The underlying understandings for this activity have to do with gravity and an object falling towards the surface of earth. If gravity is the only influence acting, then acceleration is always downward and has the same magnitude for all objects. An object falling toward the surface of Earth will fall 32.18 fee per second faster every second (32.18 ft/s^2). Students will explore how area of an object increases the drag, which than impacts the terminal velocity (so parachutes have a lower terminal velocity than say a bullet).

Students will first drop a book and record it’s height as it falls. Then, they will drop a piece of paper from the same height and record it’s height as it falls. They will then fold the paper, and repeat the drop for each fold, which is decreasing the area of the paper and thus should decrease the terminal velocity. They will compare the data by making scatter plots and consider when the falling object might have a constant terminal velocity (speed). They will look at different parts of the graph to see where the data is in a straight line, which indicates when the force of gravity is equal to the air drag force.  It’s a fun little experiment and relevant as well.

This activity is adapted to ClassPad.net from the Fostering STEM In Education with Casio Technology, Casio 2013. The links below include the ClassPad.net version of the activity, the PDF version of the original activity, that includes more description and background information as well as calculator tips and strategies, and then a video overview of the ClassPad.net activity, showing how to create the scatter plots, zoom in and out with the plots to look for when the data is becoming linear.

  1. STEM – Floating Through Air (Scatter Plot, Drag, and Gravity)
  2. STEM Floating Through Air (PDF)
  3. Video Overview – STEM: Floating Through Air (Scatter Plot, Tables, Drag, Gravity)


The tool being used in these mini-math lessons is the FREE web-based math software, ClassPad.net.

Remember – if you want to save and/or modify any of these activities, create a free account.  Some useful links below:

STEM – Newton Knew Forces (F=ma) (Mini-Math Lesson Algebra/Algebra2)

Yesterday’s lesson was related to the motion of a pendulum and it’s graph as its swing was impacted by friction. Today we are looking at force, using a pendulum as the push (force) on an object (scooter). This is a fun little experiment that you could do with students, and in this time of home-schooling, it would be a relatively easy experiment for parents to set up with their kids. You just need some rope, a bucket full of water or even a jug of water to use as your pendulum, a door frame to swing the ‘pendulum’ from, and then a scooter or something with wheels that can move when pushed (so a wagon or a skateboard). You will also need a measuring tape, some weights to add to the scooter (three different weights), and something to mark start lines and height release for pendulum.

If it’s already sounding like too much work, don’t worry!! There is sample data in the activity, so you can still explore the mathematics if you don’t have the time to set up!!

The idea is to set up the pendulum so that it hangs from a door-frame/beam at the height of the scooter (so place scooters back end directly at where the pendulums lowest point so that the pendulum will hit the scooter and push it). Measure the weight of the pendulum bob (bucket/jug of water) before you begin. Measure the weight of the empty scooter. You then decide on a release height for the pendulum (will be the same height for each release). Mark the start position of the scooter (back end), position the scooter (empty) and release the pendulum from the designated height. It should hit the scooter and push the scooter. You then measure the distance the scooter traveled after it was hit (so from the start position) to where it ends (be sure to measure at the back of the scooter, to be consistent with the start position). The next step is to add some weight to the scooter (make sure it is secured on so it doesn’t fall off when pushed!). Repeat the experiment, record the distances and weights.  Do this for at least five different weights of the scooter – empty to heavier. (Don’t worry – I have included the PDF as well with all the detailed instructions).

Once data has been collected,then you will graph the data and look at how force and mass impacted acceleration. The goal of this experiment is to show that the rate of change of momentum of an object is proportional to the resultant force acting on the object and in the same direction.  Students will explore their table of data, make scatter plots, look at the relationships. The experiment has to do with Newtons’s 2nd Law, where Force=mass x acceleration. There are a couple things to keep in mind:

  • The pendulum weight represents the force (because you don’t change the drop height)
  • The scooter weight is proportional to the mass (because gravity is constant through the experiment)
  • The average distance the scooter moves is proportional to the acceleration
  • Weight is used in the experiment instead of mass, but for this experiment it is acceptable to deal with weight because the force of acceleration is constant throughout the activity. The weight in this activity is always proportional to the mass.

This activity comes from Fostering STEM Education with Casio Technology, Casio 2013. I have converted part of the activity (the pendulum component) to a ClassPad.net activity, which is shared in the link below and also overviewed in the video below. I have attached the complete activity, which includes a wagon-pushing activity. The PDF is the whole activity with a lot of description and calculator suggestions, as well as sample data.

  1. STEM – Newton Knew Forces (F=ma) ClassPad.net Activity
  2. STEM Newton Knew Forces (F=ma) (PDF)
  3. Video Overview – STEM Newton Knew Forces (F=ma) Mini-Math Lesson (Data & Regression)

 


The tool being used in these mini-math lessons is the FREE web-based math software, ClassPad.net.

Remember – if you want to save and/or modify any of these activities, create a free account.  Some useful links below:

Stephen Hawking – Understanding the Universe

Pi Day is a day math and science enthusiasts love, not only for all the fun Pi Day activities, but also because it was Albert Einstein’s birthday, one of the most iconic mathematicians/scientists/physicists, who developed the theory of relativity. This year’s Pi Day, ironically, the world lost another renowned physicist, Stephen Hawking. Whether you never heard of Stephen Hawking until the movie The Theory of Everything (2014) or whether you only know him from his voice on the Simpsons or Star Trek, The Next Generation or The Big Bang Theory, his death is a loss to the world of science and math.

It seems silly for me to list all that Mr. Hawking contributed, when his website does such a terrific job of that already. Here is the link to his site, where you can read about Stephen Hawking, see the many publications of his, the books he wrote, the lectures he gave (transcripts), the movies about him and with him, and videos he made. This is a great resource for teachers and students to explore.

I want to leave you with a video of Stephen Hawking talking about his love of science and as he said “I did my work because I wanted to understand the universe”.

Rest in Peace and thank you for all your contributions that have helped the rest of us understand our universe a little better.