# Question About Buoyant Force and Weight of an Object

Looking at the relationship between buoyant force and the weight of an object, I found this explanation, which makes sense

"If the buoyant force is greater than the object's weight, the object will rise to the surface and float. If the buoyant force is less than the object's weight, the object will sink. If the buoyant force equals the object's weight, the object will remain suspended at that depth."

BUT if this is true, than why is the buoyant force = weight of an object if the object is floating? Wouldn't the buoyant force be greater than the weight of the object?

When an object is floating at the surface, part of the object is not submerged in the fluid. For example, a beach ball sitting on top of the water only has a very small portion submerged. Only that portion contributes to the buoyant force from the water, compared to the entire ball when it is fully submerged. Thus, the buoyant force when the ball is fully submerged is much greater, and quickly rises to the surface.

Once it breaks through the surface, it only has a very small portion of the buoyant force from before, and at that time, the buoyant force is equal to the weight. If there was no surface, it would continue to rise.

First of all, let's explain how has the buoyant force is made:

As the pressure in deep parts is bigger than the higher parts, we can say that the forces in deep parts of fluid are bigger than the higher parts of it. so we have the force difference in higher parts and the deep parts of the fluid. so there will be a net force upwards.

$$F_2 -F_2$$=$$\;$$ $$P_2A-P_1A$$=$$\;$$ $$\rho_2gh_2A$$-$$\rho_1gh_1A$$= $$\;$$ $$F_b=Ag(\rho_ {fliud}h_2-\rho_{fliud}h_1)$$= $$\;$$ $$F_b=\rho_{fliud}V_{object}g$$

we have three kinds of buoyancy:

1-Positive Buoyancy:

Positive buoyancy occurs when an object is lighter than the fluid it displaces. The object will float because the buoyant force is greater than the object’s weight.

$$F_b=mg$$ $$\;$$ so $$\;$$ $$\rho_{fliud}V_{object}g$$=$$\rho_{object}V_{object}g$$ $$\;$$ and $$\;$$ $$\rho_{fliud}V_{objectin}$$=$$\rho_{object}V_{object}$$ $$\;$$ means that $$\;$$ $$\rho_{fluid}$$>$$\rho_{object}$$

2-Negative Buoyancy: Negative buoyancy occurs when an object is denser than the fluid it displaces. The object will sink because its weight is greater than the buoyant force.

$$F_b $$\;$$ so $$\;$$ $$\rho_{fliud}V_{object}g$$=$$\rho_{object}V_{object}g$$ $$\;$$ and $$\;$$ $$\rho_{fliud}$$<$$\rho_{object}$$

3-Neutral Buoyancy: Neutral buoyancy occurs when an object’s weight is equal to the fluid it displaces.

$$F_b=mg$$ $$\;$$ so $$\;$$ $$\rho_{fliud}V_{object}g$$=$$\rho_{object}V_{object}g$$ $$\;$$ and $$\;$$ $$\rho_{fliud}$$=$$\rho_{object}$$

hope this help!