# I need help understanding Archimedes' principle.

1. Jul 14, 2013

### threy

I want to know why does the buoyant force equal to the weight of fluid displaced and how the weight of water displaced is equal to the weight of object for free floating objects? What's buoyant force by the way?

2. Jul 14, 2013

### jhosamelly

The weight of the object is the downward force. Buoyant force is the upward force exerted by the fluid on the object. (Just like, for example, if you have a book on a table, the table exerts a normal force on the book) . For objects to float the downward force which is the weight should be equal to the upward force which is the buoyant force.

I hope you get the idea.

3. Jul 14, 2013

### threy

Yeah, I get this but I still have no idea why does the buoyant force equal to the weight of fluid displaced?

4. Jul 14, 2013

### jhosamelly

Since I think you want some mathematical explanation.

Buoyant Force = (weight of displaced water ÷ volume of displaced water) * depth * (surface area in contact with water)

depth * (surface area in contact with water) = volume of the object that is under water.

Buoyant Force = (Weight of displaced water ÷ volume of displaced water) * (volume of the object that is under water)

The volume of the object that is under water = volume of displaced water, because the object displaced the water.

Buoyant Force = (Weight of displaced water ÷ volume of displaced water) * (volume of displaced water)

Buoyant Force = Weight of displaced water

5. Jul 14, 2013

### Staff: Mentor

The fluid is displaced upwards - take a bowl of water, float something in it, and the water level will rise slightly. It takes some force to push that water up, and that force has to exactly balance the weight of the object if it's going to float at the surface.

6. Jul 14, 2013

### Staff: Mentor

Because the fluid surrounding the object does not know that the object has replaced the water that was there previously. The surrounding fluid was supporting the weight of the water that was there previously. So now it is applying the very same distribution of forces to the object.