If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## AP®︎/College Physics 2

### Unit 1: Lesson 2

Buoyant Force and Archimedes' Principle

# Archimedes principle and buoyant force

Introduction to Archimedes' principle and buoyant force. Created by Sal Khan.

## Want to join the conversation?

• shouldnt we take into account the weight of the cube? i mean the forces down shouldnt they be from water pressure at the top + m*g? •   What he calls the net force in this video should be called the buoyant force. The net force is the sum of the buoyant force and the weight of the cube. So, for example, if the cube is made of pure water, its weight will equal the buoyant force in magnitude (opposite direction), and the net force will be zero. If the cube is made of steel (denser than water) the weight will be greater than the buoyant force, so it will sink. If its made of wood (less dense that water) it will float to the top.
• 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? • does that mean the pressure in me helps me not to be squashed by the atmosphere • 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." • 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.
• At the beginning, after Sal draws the cup, he puts a dot with arrows pointing to it. What is that? Pressure? • Its to illustrate that even though pressure increases with depth, the pressure at a given depth acts through all directions. If you were shrunk down to the size of a point, and placed at a particular depth, you'd feel the same pressure at that depth all around you. It wouldn't be coming from just one direction.
• 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.
• 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?   