Finding a Numerical Theory
On this page we will model a see-saw using a meterstick. There is a fulcrum with a mass on each side of the fulcrum, just like a seesaw.
For this exercise we will fix the fulcrum at 50 cm, the mass of M2 at 20 g, and the distance of M2 from the left end of the meterstick at 80 cm. The notation M2D represents the distance of M2 from the fulcrum, which in this case is set at 30 cm (M2D = 30 cm).
You will change the mass of M1 (initially 15 g) and the position of M1 (initially 10 cm) to get the meterstick to balance. When you change the position of M1 and get it to balance, the distance of M1 from the fulcrum will appear in a table below the diagram and be represented by M1D (initially M1D = 40 cm). Click on the Input Data button below to see the chart with the first experiment's data.
Increment the mass of M1 and get it to balance at least five times, always using integers for the masses. When you change the mass, the distance from the fulcrum must also change. Guess what the new position should be and try it. If it is the correct distance it will say "Good Job! It is Balanced!", and record the numbers in a table. But if it isn't the correct position, it will say "Sorry! It is not Balanced" and it will tell you if M1 would go up or down. Keep trying until you find the right positon where it is balanced for that mass.
Determine the position where the mass balances for at least five different masses and use the data from the table to come up with a single idea (a relationship that comes from the numbers in the table) that is common to every balanced situation. Write down the data and a statement of the idea with examples and submit it in the box below. You might think, for instance, that the sum of the mass and the distance from the fulcrum must always be the same (M1 + M1D = M2 + M2D).