Purpose:
One purpose of this lab is to explore the concepts and mathematics associated with circular motion. In particular, an understanding of centripetal acceleration and centripetal forces will be needed. The other principle purpose of this lab is to explore the process of using physics within a set of design constraints. This replicates, in a very simplified fashion, the use of science in the bulk of commercial and industrial situations.
Procedure:
For this lab you will need pencil, paper, creativity, and your minds. It would also be helpful to understand something about circular motion and the forces associated with it. You will design a space colony in the "trash can" style that satisfies the following constraints:
JupyterLab Notebook: Here is a link to the notebook for this lab on the github.
1) The "weight" of a person walking about on the inside of colony is equal to their weight on the surface of the earth. This is a comfort and health issue since our bodies tend to debilitate quickly in the absence of gravity.
2) The apparent acceleration 20 m above the "ground" must be no less than 95% of what they experience on the "ground". If this were not true your head might experience a very different sense of gravity compared to your feet leading to significant disorientation.
3) The total surface area that satisfies condition 1 must be 0.8 km2 and as wide as possible. The residents need some room to comfortably move around.
4) The colony must rotate in a period greater than 30 s.
5) The colony will be located at one of the Lagrange points of the earth-moon system. This means is that it will not experience any linear accelerations although there will be a centripetal acceleration due to the motion of the space colony about the earth. Determine the centripetal acceleration due to the orbit of the space colony around the earth and show that it is NOT a player in your design calculations.
Extra) Determine a reasonable number of inhabitants for your colony. Determine a reasonable volume for your colony based on the number of inhabitants.
LAB DELIVERABLES:
I) Show a clear sketch of your design. You may do a group drawing and copy it for each individual lab report. Be sure to indicate all relevant dimensions and where the living surface is that meets all of the constraints of the problem.
II) Describe the process by which you arrived at your solution. Show a clear progression or flow chart that makes it clear what you did first, second, and so on. Describe which design constraints interact with other constraints and how. Which constraints have the least impact on the design.
III) Present the calculations that support your design. This section should clearly indicate how you mathematically satisfied each design constraint. Also present your calculations that show that the accelerations due to motion around the earth are negligable in your design.
IV) Consider the following experience a resident might have. Suppose you "drop" a ball which you are holding stationary in front of you. Consider the forces on the ball and describe its motion after you release it. Calculate the "drop" time for the ball and compare it to the drop time here on earth. You will need to do some geometric thinking here. Present your analysis clearly with drawings.
