Physics Archimedes Principle Buoyancy Forces

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Density Examples A rectangular piece of metal measures 3.0 cm x 5.0 cm x 4.0 cm and has a mass of 750 grams, what is the density of the metal?

Density Examples A rectangular piece of metal measures 3.0 cm x 5.0 cm x 4.0 cm and has a mass of 750 grams, what is the density of the metal?

Archimedes’ Principle 287 – 211 BC At the moment of Archimedes’ famous discovery.

Objectives Students will be able to: Identify the factors that effect the buoyancy force. Determine the relationship between the amount of fluid displaced and the relative densities of the fluid and the body that is displacing the fluid. State and apply Archimedes Principle.

Area & Volume of Object r L

“Coke Floats” I have here two identically sized cans of soft drink made by the same company. One is a diet drink and one is a regular drink. What do you think will happen when I place each of them in this container of water?"

“Coke Floats” The cans contain the same total volume Reasoning: The cans contain the same total volume Artificial sweeteners weigh much less than sugar in equal volumes and that the amount of sweetener used in diet drinks is much less in volume than the amount of sugar used in regular drinks. Therefore diet drinks are less dense, more buoyant, than regular drinks.

Buoyant Force Buoyant Force - The upward force from a fluid exerted on an object immersed in or floating on the fluid The idea of Density or Buoyancy explains why objects float. In terms of density, objects float because they are less dense than the liquid they are floating in. In terms of buoyancy forces, objects float because the buoyancy force is greater then the weight of the object.

Weight = Force of Gravity Weight is the force due to the Earth’s gravitational pull on an object. The unit of mass is the kg. The unit of force is the N = kg x m/s2. W = Fg = mg g = 10 or 9.81 m/s2

Buoyant Force FB = rVg Where does it come from? there are two equations (P=F/A, P=rgh) set the two equations for P (pressure) equal to each other. F/A = rgh F = A(rgh) remember that volume, V = A x h therefore we can substitute FB = rVg 1

Buoyant Force The buoyancy force = the weight of fluid displaced FB = fluid g Vdisplaced Weight of object, W = mg g = 10 m/s2 object sinks if W > B (negative buoyancy) object floats if B > W (positive buoyancy) Eureka! If an object floats…. B = W (neutral buoyancy) Therefore fluid g Vdisplaced = mg

Objects sink or float based upon? Block of Steel made into a boat Block of Steel Shaping the block into a hollow form increases the volume occupied by the mass, which results in a reduced overall density, a larger buoyancy force! The ship floats. A block of steel is denser than water, so it sinks.

Archimedes’ Principle The buoyant force on an object in a fluid is the upward force equal to the weight of the fluid that the object displaces

Archimedes’ Principle

Classic Question ?

Archimedes’ Principle Suppose you have two identical bowls, A and B, filled to the brim with water. You carefully lower an apple into the water in bowl B. This causes some of the water to spill out of the bowl, but when you are done the apple floats in the remaining water and the level of the water is still at the brim of the bowl. If you carefully place the bowls on a balance, which weighs more? ?? A) Bowl A weighs more than bowl B. B) Bowl B weighs more than bowl A. C) Bowls A and B have the same weight.

Archimedes’ Principle A 200-ton ship enters the lock of a canal. The fit between the sides of the lock and the ship is so tight that the weight of the water left in the lock after it closes is much less than 200 tons. Can the ship still float if the quantity of water left in the lock is much less than the ship’s weight? 1. Yes, as long as the water gets up to the ship’s waterline. 2. No, the ship touches bottom because it weighs more than the water in the lock.

Archimedes’ Principle What matters is not the weight of the water left in the lock, but the weight of the water forced out of the lock by the ship. As long as the density of the ship is less than that of water, and the water gets to the waterline, it floats.

The photograph displayed above is one of a real structure, a kilometer-long "concrete bathtub" water bridge over the Elbe River in Germany.

Decreases from 22 N to 14 N, a reduction of 8 N. Mass suspended from Spring Scale When the mass is lowered into the water, what will happen to the reading on the spring scale? Increase Decrease Stay the same 22 N Decreases from 22 N to 14 N, a reduction of 8 N. This is the buoyant force equal to the weight of the water displaced. 14 N

Vacuum 22 N If the block and spring scale were moved to a vacuum chamber, would the reading on the scale A. Increase B. Decrease C. Stay the same Reading would increase. Archimedes principle applies to all fluids including air. In a vacuum there is no air, so there would be no buoyancy force acting on the block and therefore the reading will increase.

Archimedes Principle On a lakeshore, Leon finds a log that has a diameter of 0.16 m and a length of 2.0 m. He rolls the log, weighing 280 N, into the lake. What is the maximum weight the floating log can carry on top of it without submerging?

Archimedes Principle On a lakeshore, Leon finds a log that has a diameter of 0.16 m and a length of 2.0 m. He rolls the log, weighing 280 N, into the lake. What is the maximum weight the floating log can carry on top of it without submerging?

Archimedes’ Principle A piece of metal hanging from a force scale is placed into a graduated cylinder and the water level changes as indicated in figure 1. The force scale in air shows that a force of 7.5 N is applied, when placed into the beaker of water the force scale reads 6.8 N as shown in figure 2. Determine the buoyant force acting on the metal and the weight of water displaced by the metal. 6.8 N 7.5 N Figure 1 Figure 2

Archimedes’ Principle A piece of metal hanging from a force scale is placed into a graduated cylinder and the water level changes as indicated in figure 1. The force scale in air shows that a force of 7.5 N is applied, when placed into the beaker of water the force scale reads 6.8 N as shown in figure 2. Determine the buoyant force acting on the metal and the weight of water displaced by the metal. 6.8 N 7.5 N

Buoyancy Forces What does a single person submarine, which has a volume of 12 m3 and has a mass of 25000 kg, have for an apparent weight while submerged in the ocean? (ρsalt water=1250 kg/m3)

Buoyancy Forces Tom and his friends want to go fishing in a rowboat that has a volume of 2.5 m3 and a mass of 75 kg. How many of his 50 kg friends can get into the boat before the boat sinks?

Archimedes Principle