Physics Buoyancy And Pressure: Study Problems

1. A barge is carrying a load of gravel along a river. It approaches a low bridge, and the captain realizes that the top of the pile of gravel is not going to make it under the bridge. The captain orders the crew to quickly shovel gravel from the pile into the water. Is this a good decision? Solution: Assume an object has a weight w and a density r greater than that of water. When the object floats in a boat, the weight of the water displaced because of this object is equal to the weight of the object. When the object sinks when thrown overboard, the weight of the displaced water is less than the weight of the object. An object with r > rwater of a given weight displaces more water when floating than when being submerged. When a given volume of gravel is shoveled into the water, a larger volume of the ship will rise out of the water. But that does not necessarily mean that the maximum height h of the load above the water's surface increases. This maximum height h depends on how the load is distributed. If the load is evenly spread over the entire deck of the ship, the shoveling sand into the water is not a good idea. But if the load is a pyramidshaped pile, then removing the top of the pyramid is a good idea. 2. You are in a boat on a perfectly calm lake. There's an anchor in the boat. You drop the anchor overboard and it sinks to the bottom of the lake. During this process, does the level of the lake rise, fall, or stay the same? Solution: The anchor in the boat adds to the boat's weight, and the presence of the anchor there causes a displacement of an amount of water that weighs as much as the anchor. (The upward buoyant force due to the displaced water has the same size as the weight of the anchor, by Newton's law.) I.e., the anchor in the boat displaces a weight of water equal to its own weight. When the anchor is at the bottom of the lake it displaces an amount of water equal to its own volume. Its weight is greater than the weight of an equivalent volume of water (that's why it sank), so it displaces more water when in the boat than when at the bottom. The water level of the lake drops when the anchor is thrown overboard. 3. You are in a boat on a perfectly calm lake. A floating log passes near. You grab the log and put it in the boat. During this process, does the level of the lake rise, fall, or stay the same? Answer: The floating log displaces its own weight of water. The log in the boat displaces its own weight of water. The level of the lake is unchanged. 4. You are in a boat on a perfectly calm lake. A wooden log is in the boat, and the anchor is at the bottom of the lake. This is the same log as in the previous problem, and it would float on the water if simply tossed overboard. But instead, you raise the anchor, tie the log to the anchor, and drop both overboard, the anchor pulling the log to the bottom. Consider the entire process, from (A) when the log was in the boat and the anchor was on the bottom, to (B) when the log and anchor were both on the bottom. During this process, A to B, does the level of the lake rise, fall, or stay the same? Answer: The log in the boat displaces its own weight of water. The log at the bottom displaces its own volume of water. Its weight of water is less than its volume of water (that's why it normally floats), so the level of the lake rises. The anchor was at the bottom before and also after, so it causes no change in the lake level.