Hey guys. In this video, we're going to start talking about buoyancy, the phenomenon that causes objects to float or be pushed up when in a liquid. Let's check it out. Alright. So, if you have an object immersed in a liquid, it will be pushed up by a force called buoyant force, which stems from the phenomenon of buoyancy, usually associated with floating. We will denote this force as \( F_b \). This happens due to a pressure difference between the top and the bottom of an object submerged in a liquid.

Let's say you have a box completely submerged underwater; the water applies pressure from all sides. The force on the left will cancel the force on the right because they are at the same height. Thus, the side forces have no net effect, but the top and bottom forces will differ due to varying pressures. The deeper under the liquid, the greater the pressure. Thus, the pressure at the bottom is greater than at the top, causing the net upward force, or buoyant force. That results in a stronger force upwards than downwards, and the net buoyant force is directed upwards. Cool?

Next, you should know Archimedes' principle, which states that the magnitude of the buoyant force is the same as the weight of the liquid displaced. However, to calculate this force, we use the equation \( F_b = \rho_{\text{liquid}} \cdot g \cdot V_{\text{under}} \), where \( \rho_{\text{liquid}} \) represents the density of the liquid, \( g \) is gravity (approximately 9.8 m/s² on Earth), and \( V_{\text{under}} \) is the volume of the object submerged in the liquid. Remember, the important volume is the volume underwater, not the total volume, unless the object is completely submerged.

The more an object is submerged, the greater the buoyant force acting on it. We also need to define the density of an object, which is mass over volume. In equations, this involves the total and submerged volumes, leading us to consider both in various scenarios. For most buoyancy problems in physics, they reduce to a force problem where the sum of all forces equals zero, especially when objects are at rest or equilibrium in a liquid.

As an example, imagine an object fully submerged in a large water tank. When it's released and reaches equilibrium, 30% of its volume is above water. From this configuration, we estimate the density of the object using our equations and understanding of volumes. By setting the net force equation to zero and expanding terms, we determine the unknown density after a series of substitutions and simplifications, concluding with the object's density based on its submerged volume and known liquid density.

This presents a clear example of how evenly basic physics principles like buoyancy apply in detailed, practical scenarios and demonstrate the consistent application of principles like Archimedes' principle and fundamental force analysis.