Pendulums are wonderful physics toys that are great for exploring periodic functions. For week 49, I encourage learners to get out some string, weights, and stop watches.
Here are some ideas for playing with math and pendulums:
Start with a string and a weight to observe basic pendulum motion. Nuts, bolts, tennis balls, and other objects can work as weights.
Record how long it takes for the pendulum to return to its start (this is called the period).
Change the length of the string to see if it changes the period.
Change the mass of the weight to see if it changes the period.
For older learners, you may want to try to find the relationship between time, period and length.
With all ages, it can be fun to look at trigonometric functions with this activity.
Another activity is to create a wave pendulum. This can be done with a broomstick and weights, or other construction toys. I like to bring in a maker box and materials and have learners devise a way to make a wave pendulum. Once you have one working, then see if learners can explain why it’s called a wave pendulum. For those that like to code, look at creating a wave pendulum . My code is here and running below. At the bottom of this post I have a portable laser cut pendulum I designed.
Another activity is a painting pendulum. Hang a cup full of paint over a canvas and push it into a circular motion and watch the curves that are created as the pendulum is dampened. These can be a lot of fun with large tripods in bigger spaces.
Finally, I love to create chaotic pendulums because they are such a contrast to the previous activities. To create a chaotic pendulum, you can use building toys to create a tripod with a pendulum and then put a magnet in the weight. Put other magnets just beyond the reach of the pendulum and kick it off. The motion observed will be nothing like the periodic and predictable motion of the previous exercises. This is a great opportunity to talk about dynamic systems, chaos, and unpredictable behaviors.
Another topic that can be discussed is how pendulums dampen and why they do. What would happen in a vacuum?
You don’t have to be in high school math to play with conics, orbits, and projectile motion. This week (or month) learners can play with projectile motion, orbits, and conics sections with the activities below:
1.) Slicing cones
Learners can mold cones with clay and slice to see the possible shapes. This will give circles, ellipses, parabolas, and hyperbolas.
Create a cone sculpture with an intersecting plane using paper, string, pipe cleaners, or other mediums.
Create a straw rocket (don’t aim it at someone) and take slow motion videos of their flight and observe the curve that is created. For a template and activity, go to NASA’s website here. Look at various launch angles and analyze the differences and similarities in curves.
Create a water balloon launcher with PVC pipes (or other parent/teacher approved apparatuses). Record their launches and analyze. (Water rockets are also fun.)
Play with a garden hose and the curves created by shooting water up into the air.
In math we find balance and equilibrium. We balance equations. We keep balance by using properties of identity (multiply by 1 or add zero), Properties of Equality (mirroring operations), and by using the many other ways to manipulate and play with structures in math.
This week’s math is about equilibrium through building tensegrities (see photo above). Buckminster Fuller coined the term “Tensegrity” by combining “tensional” and “integrity.” He described the structure as, “Islands of compression in an ocean of tension.”
For this week’s activity, grab building toys, hot glue and sticks, or straws and string to create tensegrities. Learners can work on the simple design in the photo above, or on polyhedrons, bridges, sculptures, and more. Some challenging shapes would be polyhedral structures or towers. The goal is to create a structure that uses the tension of strings and the weight of the objects in positions that reach equilibrium.
For high school or middle school students, force diagrams may be a fun activity as well. Think about the moments and forces that balance in each structure created. There is a great “Beyond the Brick” video here. For strings at angles, there are some great trigonometry applications to play with.
I have decided to start a new category on this blog for my “makings” – items and projects that I have designed/created for classroom use, art, fiber musings, or just because.
Today I decided to create an easy to store, easy to demonstrate, easy to build wave pendulum. I’ve built these in STEM classes, homeschool, and in groups with wood, broom sticks, tennis balls, and a whole bunch of nuts (hardware).
I decided to joint it with orthodontic rubber bands and I used sewing thread to hang the weights. I went with sharp triangles to hold the thread and found that I don’t have to tie it. This one is acrylic, but I am contemplating a wooden one.
I am selling the SVG file for this project here to be able to support the site and equipment.
Here are my pictures: I know the orange is a bit of an eyesore, but I love it for this sort of stuff.
This week we are going to take a look at applied math. Learners will be given a ramp (this can be a ruler), a ball that fits on the ramp, measurement device (ruler) and a timer. With these instruments learners can investigate the relationship between distance and time as the ball rolls down the ramp. I encourage teachers and facilitators not to give too much procedure here and let students come up with the way they will execute an experiment and record their data. I usually go with a 10-15 minute “sweat-it-out” period before I give them any hints.
This exercise is a great intro into calculus concepts like “instantaneous velocity” and derivatives of functions that model falling bodies. I think this is fun to do with middle schoolers and up. You can plot your functions and then draw the tangents to the curve and find slopes (this is fun in groups).
If students are stuck, hints may look like this:
Have you set up an experiment that you can repeat to get multiple samples?
What time intervals are you going to try to record? how far has the ball rolled with zero seconds? 1 second? 2 seconds?
Once you have your data, can you plot it to see if there is a relationship? Is it a direct variation?
If you plot the relationship, what type of curve is it? Can you create a function for that curve?
Here is a sheet I had for a class that students received after completing their experiments: