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Archimedes' Principle: Measuring Buoyant Force


Today we're going to talk about another example of fluid static and that is Archimedes' principle, Archimedes' principle that if an object is immersed in liquid either partially or fully then because of the increase pressure in the lower depths of the fluid and higher points of the fluid there will be a net upward force on the immersed object and that's called the buoyant force. Archimedes principle states that the buoyant force is equal to the weight of the fluid that's displaced by the object. And by writing it this way we have written that the weight has the mass of the fluid density of the fluid times the volume of the fluid times the gravitational constant g.

In this example of Archimedes' principle we're going to take this brass lock and I'm going to suspend it from a scale. The scale reads the tension force that's pulling upward on the brass block and when the block is just suspended in the air, the upward force of the spring simply balances the downward force of gravity. So this is reading the weight of the block, which in this situation In this situation the spring scale is reading about 3.4 Newtons as you can see that must equal the weight of the block. I'm going to dunk this block into a container of water and anytime it is even partially immersed in the water there will be an upward force from the water a buoyant force that will cause the reading of the scale to decrease as we can see from the force diagram. There will be three forces on that block, there will be a tension force from the string there will be the force of gravity mass of the block times g and once it's in the water there will be an upward buoyant force according to Archimedes' principle. The weight doesn't change, so if the buoyant force increases as I immerse the object than the tension force must decrease since all three forces are balanced in the blocks equilibrium.

Okay so let's watch what happens, actually before we watch, let's predict what's going to happen. So, I want to do with you a calculation of how much the buoyant force should be. Archimedes' principle says that that should equal the weight of the displaced water we can calculate that because we know the density of the water is about 1000, 103, milligrams per meter. The volume that will be displaced by this block is equal to the weight of the block. And so the length of one side of that block is about 3.1 centimeters 0.031 centimeters the volume of the block is that power, that distance cubed. And the gravitational constant g the earth's surface is about 9.8 N/kg. According to Archimedes principle, if you do this calculation you'll see that the buoyant force should be about 0.3 Newtons when you multiply those numbers. Let's test that prediction; here you can see the scale reading about 3.4 Newtons, and I'll try to keep this in equilibrium the whole time. Alright now the block is completely immersed and you can see that the scale reading is now about 3.1 Newtons, in agreement with our prediction. If I take the block back out the scale reading goes down.

Now another interesting fact related to Archimedes' Principle if the fluid exerts an upward buoyant force on the block according to Newton's third law the block must also exert an equal force in the downward direction on the fluid. We should be able to measure that force by putting a scale under the fluid. The bottom scale here right now is measuring the weight of this fluid plus this container its recording that in grams by converting that to a mass. When I immerse this block there should be a downward force on the fluid of about 0.3 Newtons the force will equal to the buoyant force that the fluid exerts on the block. So the bottom scale reading should actually go up, due to the downward force of the block. So we should see that scale reading on the bottom scale go up; it went from 2.72 to 3.05 that's about 30 grams almost and corresponding to a weight of about 0.3 Newtons as we predicted.

For one more example of Archimedes' Principle I'll show you another block of identical volume but different materia;, this is aluminum so it doesn't way quite as much as the brass. It weighs about 1.5 Newtons or so. When I immerse the aluminum in the water it will displace the same amount of water so the buoyant force should be the same. And in this situation, the scale reading should decrease by the same amount, 0.3 Newtons, as it did for the brass. There we go so, the scale reading should be now about 1.2 Newtons and the bottom scale again increased to about 305 grams.  

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