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## Physics library

### Course: Physics library>Unit 9

Lesson 2: Buoyant Force and Archimedes' Principle

# Archimedes principle and buoyant force

Explore Archimedes' principle and the buoyant force in fluid dynamics. Understand how pressure varies with depth and acts in all directions, leading to the upward net force on submerged objects. This principle explains why objects float and is key to fluid displacement and the concept of buoyancy. Created by Sal Khan.

## Want to join the conversation?

• I am confused because I thought at the beginning of this lecture Sal said that the pressure around a submerged object was equal from all directions but at the end of his lecture he says that the pressure is greater underneath the object than on top and that is the buoyant force. Could someone help clear this up for me? What is Sal actually saying?
• His first example was a point, which has a volume of zero. Around this point the pressure is equal because no volume of liquid is displaced. Also, a point has no "height", hence no difference between pressure up and bottom. In the cube example, it has volume, which generates difference in pressure up and bottom.
• does that mean the pressure in me helps me not to be squashed by the atmosphere
• yes!
• This question appeared in my physics final paper and there is confusion amongst students over its answer: "A wooden block is lying on the bottom of the tank sticking (with glue) to it. When water is poured into the tank, water does not enter below the block. Is there a buoyant force acting on the block? Explain."
• Short answer, no. Remeber how suction cups works. because the rubber doesn't let any air under the cup, the pressure of atmosphere is what making it stick to a surface. Same rules apply here
• Does an object (such as a hot air ballooon) float because it weighs less than a volume of normal air equivalent to the volume of space it takes up? Also, as the air is heated up by the balloon, it becomes less dense and it should float. But what exactly is pushing it up--is it the hot air itself pushing upwards on the inner walls of the balloon?
• There are two explanations as to what is pushing up the balloon. One is that atmosphere (which is a fluid in static equilibrium) cannot distinguish between the balloon and an equivalent amount of normal air in its place. Therefore, it provides an upward force due to difference in hydrostatic pressure at the bottom of balloon and the top, which is equal in magnitude to the weight of normal air the size of the balloon. Had there been normal air there it would have been static as the upward force would have been equal to its weight but since the weight of the balloon is less than the upward force acting on it, it will move up. This is what concept of floating and upthrust is. The second explanation is considering the tendency of the entire system to lower its gravitational potential energy which can be done if the balloon were replaced with air (due to its greater mass) and therefore all elements of air above the balloon, try to reduce the net energy by coming down in place of the balloon and in the process providing an upward push on it.
• if I exhale completely, I sink to the bottom of a pool. If my lungs are full of air, I float. Is this simply due to the fact that the volume of my body is greater when my lungs are full of air, and thus my overall density is less? Is there not some other buoyant property afforded by the fact that my lungs are full of a low-density gas?
• When you inhale, you increase your volume, which makes you displace more water, which increases the buoyant force on you. The air you inhale has very little mass, so it doesn't really add anything to your weight. The net upward force increases.
• I've seen people write things like "Archimedes' principle says that the buoyant force acting on an object is equal to the weight of the liquid displaced. This simply means that if something is denser than the liquid, it will sink." I've tried figuring out how they came to that conclusion and did a considerable amount of research on it, but I could never figure it out. How did they come up with that?
• This is something difficult to visualize. But here is how to get there:

The force of water above the object is given by rho*g*h, and the buoyant force underneath the object is equal to the (pressure at the bottom of the object)*(surface area of the bottom of the object). Let's look a little closer at that surface area. The surface area is related to the volume; generally, the greater the total surface area of an object, the greater the object's total volume. For example, an empty balloon has a much smaller surface area than a balloon filled with air. Why did the surface area change? Well, that's because we increased the balloon's volume!

Now, if an object has a greater density, that means that, per amount of surface area, that object also has a greater mass for that given area. If that amount of mass on the surface of the object is greater than the mass of the area of the water (or any liquid) underneath it, then the gravitational force pulling downwards on the mass of the object will cause the object to "push aside" the liquid in its way.
• At , to summarize Archimedes principle- for every submerged object the weight of water displacement equals the object's weight? Is that right? Thanks.
• No. Nothing was talked about the object's weight. It summarizes saying that the buoyancy force acting on the submerged object is equal to weight of displaced liquid, which depends only on the volume of the object. That is not the only force acting in the object though, there is also the object's weight but it was not mentioned so far.
• how does he know that the pressure of the cube at the bottom is higher than the pressure on top?
• Pressure is directly proportional to the depth below the surface of the liquid. The deeper we go down, the higher the pressure. The larger the cube, the more the pressure difference between the top and bottom.
• At , Sal says the net upward force of submerged objects equals the weight of liquid displaced. Would it be accurate to say this applies to gases too since we're talking about weight, and possible compression wouldn't change weight?