In this lesson, students build off past lessons, including Playing "A-Round" with Circular Motion and Can You Make the Turn. Students build on past understanding of circular motion when they apply the concept of centripetal force to objects that seemingly "stick" to the inner edge of a rotating object. This phenomena is commonly used in amusement park rides that spin people around and has been used many times in science fiction stories as a way to create artificial gravity in a space ship.
To complete this activity, students use CCSS Math Practice 4: Model with Mathematics and NGSS Science Practice 2: Developing and Using Models as they apply the equations of centripetal force to design a rotating space habitat. NGSS HS-ETS1-3 is applied here where students must "evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a constraints, including cost and safety". This is in the context of NGSS performance standard HS-PS2-1 as Newton's 2nd Law is the central to their analysis.
At the beginning of class, I display the first slide of Spaceship Design Challenge power point, which is a brief review of the central formulas and concepts of uniform circular motion. This slide serves to remind students of those core ideas. Then I ask how many students have spun a container of liquid upside down fast enough so that it does not spill. With a cup of water in hand, I spin it in a circle over my head. Then I say, "Did you ever wonder why is it you can spin a cup upside down, and nothing comes out. But without it spinning, the water falls out?" I hold the cup of water over a sink and dump it out to make the point. I do this to activate student thinking and remind them of their own past experience as most students have done this before.
I refill the cup with water and hand it to a student and ask them to confirm for the rest of the class that does indeed contain water. Then I pull out the platform and cup of water (see picture). For some reason the platform at the end of the strings add drama to the demo. Though they know the water stays in the cup when I hold it in my hand, they are not sure it is going to work on the platform. I try to increase the drama as I gently swing the platform with cup back and forth asking, almost as if to my self, "Do I dare?" and sprinkle in self-doubting comments like "This will make a big mess when I spill it." and "What if it goes horribly wrong?" This builds tension in the room and students love it!
Then I effortlessly swing the cup and platform all the way around, never spilling a drop. I do this a few more times to show the students it was not a fluke and and the water stays put inside the cup, even though the cup goes upside-down.
I then demo a linear example with a much less messy version: a cup and ball. If I hold the cup upside-down the ball falls out. But, if I accelerate the cup downward faster than 9.8 m/s^2, the ball doesn't fall out. The ball stays in the cup because I am accelerating it and the cup faster than gravity does.
I switch to the 3rd slide of the Spaceship Design Challenge power point which shows a free-body diagram that supports my explanation. The cup and water going in a circle is similar to the cup and ball going straight down. The only difference between the two situations is that the cup with water goes round in a circle and the cup with ball goes straight down. If I spin the cup and water so that its centripetal acceleration is greater than g (9.81m/s^2), the centripetal force, which is a normal force, keeps the water in the cup.
This demonstration sets the scene for the next activity where a centripetal force, which is a normal force in this case, allows people to walk along the inside edge of a rotation space ship.
Now that students understand that a normal force can keep an object against the inside edge of a rotating object, we are going to apply that idea. First I want to have students relate more first hand experiences to the concept of circular motion as they explain their experiences on amusement park rides.
There are many amusement park rides where centripetal forces act on the occupants. I ask students to provide examples where they have been on an amusement park ride that goes in a circle. As students volunteer their answers, I ask them to describe the ride and their experiences on such rides. This activates student thinking as it relates to centripetal forces "sticking" them to the inner edge of the rotating surface. It is especially valuable, because students can relate real-life experience to this activity.
For decades, science fiction writers have been using this concept of centripetal forces for creating artificial gravity in space. I show the Youtube clip from the movie, "Mission to Mars" which shows a scene of a rotating spaceship that creates Earth-like conditions. It is an example of excellent cinematography and is very convincing. This clip is linked in the picture of the spaceship in Spaceship Design Challenge power point; clicking on that during the lecture brings up the short movie clip. I then show the next slide on the power point which has a variety of sci-fi books and video games that have used centripetal forces to create artificial gravity.
Then I provide students with the design challenge, detailed on the Spaceship Design Challenge power point. Working in teams of two, students are to design their own spaceship! The only requirement they must meet is that the ship, or part of the ship, rotates in such a way that it creates an Earth-like artificial gravity condition (centripetal acceleration = 9.8m/s^2). Outside of that one requirement, the students can imagine any shape and size they want; there are no other restrictions, as the resources available to build the ship are unlimited.
I pick teams of two because the students can bounce ideas off of each other and together design something really special. Also, it helps with the application of physics and math, as some students are not sure how to approach the calculations. I let students choose their own partners as they have more fun working with a friend or someone with whom they are familiar. This allows them to be less inhibited in their design ideas.
While students are working on this project, I go from group to group and provide help where needed. For groups or classes that need more scaffolding on the math or physics side of the project, I give them the Space Ship Design Challenge worksheet which provides more structure than is on the power point slide. This is a differentiation piece that provides support for struggling students.
At the end of the period, I collect the students spaceship designs. Because of the open ended nature of this assignment, students can choose any size ship they want, I use the period and velocity calculations spreadsheet as a reference for correcting the student work. For any chosen radius, there is one correct value for the rotational period and tangential velocity if students are to create Earth-like conditions.