K

Krish Gupta

Daniella Garcia-Loos

As we have introduced before, buoyancy is the force caused by a difference in pressure at the top of the object and the bottom of the object.

Since pressure increases with depth, there is greater pressure pushing the object up then there is pushing it down. This net upward pushing force is called the buoyant force (also called the force of buoyancy). ๐โโ๏ธ

To find the strength of the buoyant force, we use Archimedes' Principle: the magnitude of the buoyant force is equivalent to the weight of the displaced fluid.๐ฃ๐ผโโ๏ธ

Letโs try to understand this fundamental principle with an example. Say we have a bucket full of water, and we put a baseball in the water. Some of the water will spill out as the baseball takes up space. The weight of that spilled water is equivalent to the strength of the buoyant force on the baseball.

Find the net force on a box weighing 15 kg and with a volume of 0.2 m^3 when put completely under water.

The buoyant force on the ball is simply the weight of water displaced by the ball:

Fb=Vbox*ฯwater*g = (0.2m3)(1000kgm3)(10ms2)=2000N

The force ofย gravity on the ball is:

Fg = mg = 15kg(*10ms2) = 150N

These forces oppose each other, so we can say:

Fnet = Fb โ Fg = 2000N โ 150N = 1850N

Archimedes used this fact to prove to a king that his crown was not made of gold (gold is very dense) and that he was actually being scammed by the jeweler. ๐

Here are some key points about buoyancy:

- Buoyancy is the force that acts on an object submerged in a fluid, causing the object to float or sink.
- Buoyancy is an upward force that is equal to the weight of the fluid displaced by the object.
- The buoyant force acting on an object is equal to the weight of the object when the object is in equilibrium, meaning that it is either floating or sinking at a constant velocity.
- If the buoyant force acting on an object is greater than the weight of the object, the object will float. If the buoyant force is less than the weight of the object, the object will sink.
- The buoyant force acting on an object depends on the density of the fluid and the volume of the object.
- Archimedes' principle states that the buoyant force acting on an object is equal to the weight of the fluid displaced by the object.

Apparent weight is another important quantity that you can be asked about on the AP exam. Apparent weight is the weight of an object in a particular fluid.

For example, try lifting your friend and sibling up in the air. The force you have to overcome is their entire weight. Now try to lift the same person in a pool. Isnโt it much easier? But why is that? Isnโt gravity still pulling with the same strength? It feels easier because the buoyant force is helping you push against gravity. ๐ Therefore, the apparent weight (Wa) of the object is the difference between its true weight (Fg) and the buoyant force (Fb) acting on it.

Here are some key points about apparent weight in a fluid:

- In a fluid, the apparent weight of an object is the force that the object exerts on the scale or other measuring device used to determine its weight.
- The apparent weight of an object in a fluid is equal to the buoyant force acting on the object minus the object's true weight.
- The buoyant force acting on an object in a fluid is equal to the weight of the fluid displaced by the object.
- If the buoyant force acting on an object in a fluid is greater than the object's true weight, the object will float and will have an apparent weight of zero.
- If the buoyant force acting on an object in a fluid is less than the object's true weight, the object will sink and will have an apparent weight equal to its true weight minus the buoyant force.
- The density of the fluid and the volume of the object determine the buoyant force acting on the object.

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