Two cubes made of the same material of density 1.28 g/cc are connected over a frictionless pulley. The smaller cube has a side length of 5.2 cm, and the larger cube has a side length of 6.7 cm. Alone this would be something called an "Atwood's Machine," pictured with cadets in 1900 at right. It is, for the most part a way to measure the local acceleration due to gravity more precisely than you could by dropping one of the weights. Since the two weights are competing, two very closely matched weights could be used to reduce their acceleration to something manageable. Here, you will imagine that you've submerged the larger of the two cubes in a column of water of depth 23 cm, holding it on the bottom until you release your hand. Then, you will examine what happens to the acceleration as the block rises. The structure of the Atwood's machine will allow you to make some observations about buoyancy as the block rises. I. Analyze the Objects (a) What is the mass of the smaller block? m = (b) What is the mass of the larger block? M = II. At the Bottom First, look at the block at the bottom of the water column, just after you release it. (a) What is the acceleration of the block at this point? all = III. Half Way Up Now, the block has risen 11.5 cm from the bottom. What is the acceleration of the block now? (a) What is the acceleration of the block at this point? IV. At the Top The block is just about to reach the water line. What happens to the acceleration of the block? (a) What is the acceleration of the block at this point? aly = V. Starting to Emerge The block is now starting to emerge. About 1/6th of the cube pokes out (one of its flat sides pointing straight up). How does this affect the accleratin (a) What is the acceleration of the block at this point? av = VI. Half Way Up With the flat side still pointing upward, what would be the acceleration when half of the cube has emerged from the water? (a) What is the acceleration of the block at this point? avI = VII. Almost Out Now only 1/6th of the cube is still in the water. (a) What is the acceleration of the block at this point? aVII = VIII. The Emergent Cube After the cube has fully left the water, what is its acceleration? (a) What is the acceleration of the block at this point? avIII=