Buoyancy and Archimedes’ Principle

1 1 Buoyancy and archimedes Principle Assume block is in equilibrium. Then upward forces must equal downward forces. Upward force: pressure from fluid Downward force: atmospheric pressure plus weight ThereforeBuoyancy and archimedes Principle In this case, the object is less dense than the fluid, and it floats Here, the object has the same density as the fluid, and is in neutral equilibrium Now, the object is more dense than the fluid, and it sinksw >w =w < Buoyancy and archimedes Principle archimedes Principle : The buoyant force on an immersed object equals the weight of displaced = Buoyancy and archimedes Principle archimedes Principle : The buoyant force on an immersed object equals the weight of displaced fluid. The apparent weight of an object is reduced by the buoyant =2A metal sphere weights N in air and N in water. What is its density?A rectangular tub made of a thin shell of concrete has length l= m, width w= 80 cm, depth d= 60 cm, and mass mT= 200 kg.

2 The empty tub floats in a lake. How many students of ms= 80 kg each can stand in the tub before it sinks?Stability When a body floats it is because the downward force of gravity just cancels the upward force of Buoyancy . This alone is not enough; one also wants to know if the floating is stable, that is, whether the floating object might tip over. This can analyzed (and considered in the design) using the laws of In thinking about whether, say, a tilting boat will right itself, it is important to note that gravity acts as a single downward force passing through the center of mass of the body while the Buoyancy acts as a single upward force passing through the center of mass of the displaced fluid Stability is determined by the Torque (moment) caused by these two forces Stabilizing torque Pushes boat back to an upright position Tipping torque Pushes boat away from the upright positionMore Slides to Follow3 The force needed to hold the brick in The force needed to hold the brick in place underwater is: place underwater is: WW to archimedes Principle , FBis equal to the weight of the fluid displaced.

3 Since Since each brick displaces the same amount of each brick displaces the same amount of fluid, then fluid, then FFBBis the same in both the same in both BricksTwo Bricks121) greater2) the same3) smallerImagine holding two identical Imagine holding two identical bricks in place under water. bricks in place under water. Brick 1 is just beneath the Brick 1 is just beneath the surface of the water, while brick 2 surface of the water, while brick 2 is held about 2 feet down. The is held about 2 feet down. The force needed to hold brick 2 in force needed to hold brick 2 in place is:place is:Initially the chunk of steel floats by sitting in the boat. The buoyant force is equal to the weightweightof the steel, and this will require a lot of displaced waterrequire a lot of displaced waterto equal the weight of the steel. When thrown overboard, the steel sinks and only displaces its only displaces its volumevolumein waterin water.

4 This is not so much water -- certainly less than before -- and so the water level in the lake will Golden PondOn Golden Pond1) rises2) drops3) remains the same4) depends on the size of the steelA boat carrying a large chunk of A boat carrying a large chunk of steel is floating on a lake. The steel is floating on a lake. The chunk is then thrown overboard and chunk is then thrown overboard and sinks. What happens to the water sinks. What happens to the water level in the lake (with respect to the level in the lake (with respect to the shore)?shore)?Remember that we have:so if the ratio of the volume of the volume of the displaced water to the volume of the displaced water to the volume of the object is 3/4object is 3/4, the object has 3/4 the 3/4 the density of waterdensity of IArchimedes IfluidobjectobjectfluidVV =1) 1/4 2) 1/3 3) 4/3 4) 3/4 5) 2/1An object floats in waterwith 3/4 of its volume submerged.

5 What is the ratio of the density of the object to that of water?We know from before that the object has object has 3/4 the density of water3/4 the density of water. If the water is now replaced with oil, which has 1/2 the 1/2 the density of waterdensity of water, the density of the object density of the object is larger than the density of the oilis larger than the density of the oil. Therefore, it must sink to the IIArchimedes II1) it floats just as before2) it floats higher in the water3) it floats lower in the water4) it sinks to the bottomThe object is now placed in oilwith a density half that of water. What happens?4We already know that density of the object is 3/4 of the density of density of the object is 3/4 of the density of waterwater, so it floats in waterso it floats in water( , the buoyant force is greater than its weight). When covered by more water, it must therefore float to the IIIA rchimedes III1) move up slightly2) stay at the same place3) move down slightly4) sink to the bottom5) float to the topAn object floats in waterwith 3/4 of its volume submerged.

6 When more wateris poured on top of the water, the object will: With the oil on top of the water, there is an additional buoyant forceadditional buoyant forceon the object equal to the weight of the displaced oil. The effect of this extra force is to move the object upwardsmove the object upwardsslightly, although it is not enough to make the object float up to the IVArchimedes IV1) move up slightly2) stay at the same place3) move down slightly 4) sink to the bottom5) float to the topAn object floats in waterwith 3/4 of its volume submerged. When oilis poured on top of the water, the object will:A helium balloon in an air-filled glass jar floats to the top. If the air is replaced with helium, what will happen to the helium balloon?1) it still floats at the top because it has positive buoyancy2) it stays in the middle because it has neutral buoyancy3) it sinks to the bottom because it has negative buoyancy4) the balloon shrinks in size due to the surrounding helium5) the balloon grows in size due to the lack of surrounding airThe balloon floats initially because the displaced air weighs more than the balloon, so the buoyant force provides a net upward force.

7 When the balloon is in the lighter helium gas (instead of air), the displaced helium gas does not provide enough of an upward buoyant force to support the weight of the Balloon IHelium Balloon INow the jar is lifted off the table, but the jar remains inverted to keep the helium gas in the jar. What will happen to the balloon?1) it floats at the top of the jar2) it floats at the bottom of the jar, but still fully inside the jar3) it floats below the bottom of the jar, sticking halfway out the bottom4) it sinks down to the surface of the tableThe balloon sinks in the helium gas (fluid #1), until it hits the surface of the air (fluid #2). Since the balloon floats in air, it will float on the surface of the air, and therefore remain inside the jar, but at the Balloon IIHelium Balloon II5 The block in B displaces an amount of displaces an amount of water equal to its weightwater equal to its weight, since it is floating.

8 That means that the weight weight of the overflowed water is equal to the of the overflowed water is equal to the weight of the blockweight of the block, and so the beaker beaker in B has the same weight as that in Ain B has the same weight as that in in Water IWood in Water ITwo beakers are filled to the brim with water. A wooden block is placed in the second beaker so it floats. (Some of the water will overflow the beaker). Both beakers are then weighed. Which scale reads alarger weight?same for bothA floating object displaces a weight of water equal to the weight of water equal to the objectobject s weights weight. On the Moon, the wooden block has less less weightweight, but the water itself also also has less weighthas less in Water IIWood in Water IIA block of wood floats in a container of water as shown on the right. On the Moon, how would the same block of wood float in the container of water?EarthMoo