PRESSURE AND BUOYANCY CONCEPT SUMMARY So far The pressure applied to a confined liquid is transmitted to every point in the liquid (Pascal's Principle). At any given point in a liquid the pressure is the same in all directions. The difference in pressure between two points in a liquid at different depths is given by P = ρg h, where ρ is the density of the liquid. CONSTANTS The pressure at sea level due to the gas in the atmosphere is about 14.7 lb/in 2 or about 1.01 x 10 5 N/m 2. The density of water is 1 gm/ml, or 1 gm/cm 3, or 10 3 kg/m 3. STATION # 1 Beaker on a Balance Place a beaker of water on a triple beam balance, and adjust the scale s reading until the scale s lever arm is balanced. Imagine (but don t do it yet!) putting your finger into the water. Do you think putting your finger into the water will change whether the scale s lever arm is balanced? Why or why not? (If you are clueless, it s OK to say so.) Now place one finger into the water. Is the scale still balanced? Does the water level in the beaker change when you put your finger into the water? Why? Based on what we know about pressure, does putting your finger into the water change the pressure on the bottom of the beaker? the total downward force of the water on the beaker? Why does the scale behave as it does when you put your finger in the water?
Next, find the mass of a block of wood that will fit in your beaker. If you float the block of wood in the beaker, what will be the reading on the scale? Try and see. Question: How does the scale know that the block of wood is floating in the water? Definition: The upward force that the water exerts on the wood to make it float is called the buoyant force. 2
BUOYANCY 1. Hang a steel cylinder by a string from a triple beam balance that is supported by a vertical rod. Be sure to balance the scale, record the mass of the cylinder, and then calculate the weight of the cylinder. 2. If the steel cylinder is immersed in water, the scale is no longer balanced. Rebalance the scale and record its new reading. Multiply by g to obtain the object s effective weight underwater. 3. Now look at the cylinder. The top and bottom of it are at different depths in the fluid, and so must be experiencing different pressures. What is the difference in these pressures? (You will have to measure the length of the cylinder.) 4) How big is the net force exerted on the cylinder due to this pressure difference and what direction is it in? 5) Based on your answer to the preceding question, how much less should the cylinder weigh under water than out of water? 3
6) Is your answer to #5 consistent with your results in #s 1 and 2? 7) What was the total volume of the cylinder? What would the weight of this same volume of water be? How does the weight of this equivalent volume of water compare with the apparent change in weight of the cylinder? Discuss your results with the instructor. This decrease in weight is said to be due to the buoyancy of the water. It comes about because of an uneven pressure on the bottom and top of an object in the fluid. Arcihimede s Principle states that the buoyant force on an object in a fluid equals the weight of the fluid that the object displaces. STATION 3: Wooden boats Take a wooden block and a tub of water. Gently place the block in the tub of water and mark the water level on the side of the block. Then perform the following calculations: 1. What is the total volume of your block? 4
2. When the block floats in water, what is the volume that lies below the surface of the water? 3. What is the volume of the water that is displaced by the floating block? 4. Given what you know about the mass density of water, what is the weight of the water that is displaced by the floating block? 5. FROM #4 and using Archimede s principle, what is the weight of the block? Its mass? 6. What is the mass density of the block? 7. Compare the ratio of mass densities of the block and water with the fraction of the block that was submerged in the water. 5