Your next task is to build a machine that can separate two rods oating in space. These rods are aligned so that a single straight line can be drawn across both of their lengths. Both rods are uniformly dense with lengths L1 meters and L2 meters masses m1 kilograms and 771,; kilograms. Your machine will keep the closest ends of each rod separated by a distance of D meters. The following GeoGebra application simulates this effect specically when D = 4, L1 = 7,7711 2 10, L2 = 5 and m2 = 15, however your work should keep D, L1, m1, L2, and m; as variables. You may alter the "N=" slider to alter the number of sections into which each rod is broken. You may alter the "Move Sample Mass" sliders to view a sample force of attraction between any two approximate segments. Move Sample Mass 2 N = 5 Move Sample Mass G - Sample Mass 1 - Sample Mass 2 2 - 3 Sample Force 2 = _ D2 16 Sample Mass 2 : 3 D : 4 Sample Mass : 2 O O O O O O O O O O O 0 Mass 2 : 3 Mass : 2 Length = 5 Length = 7 n Mass 2 15 Sample Distance : 4 Mass 2 10 L: Part A First, use an integral to calculate the force that your machine will have to exert to keep the rods apart. Part B 1. If you copy both rods and fuse the copies to the farther ends of each rod, how much more force will your machine have to exert to keep the rods apart? 2. You will make both rods have innite length by progressively copying and fusing as described in step 1. Is there a force that your machine can exert to keep the rods apart? Why or why not? Your answer must include an account of the over and underestimates of the force as the copying process continues. Part C Suppose the rods are no longer uniformly dense. Is it possible to tweak the density of the rods (i.e. how is the mass affected by the length) so that you reverse the answer in step 2? In other words: If you found that there was a force that could keep the infinite rods apart, how can you make it so that there is no possible force? If you found that there was no force possible in Part B Question 2, how do you make it so that there is a force possible