*This summary of the video was created by an AI. It might contain some inaccuracies.*

## 00:00:00 – 00:10:45

The video delves into Archimedes' Principle to explain why certain objects float while others sink, centering on the principles of buoyancy and density. It recounts the discovery of the principle by Archimedes, who observed water displacement to determine the density and composition of a crown suspected to be adulterated. The principle, stating that an object displaces a quantity of fluid equivalent to its volume and experiences an upward force equal to the weight of the displaced fluid, is demonstrated with practical examples. Presenters José and Kukis calculate whether a cube will sink or float based on its weight compared to the thrust force. They further illustrate that reshaping an object, like transforming plasticine into a bowl shape, can alter its buoyancy. Additionally, it explains that objects like boats float by incorporating air to lower overall density. The video's insights extend to applications in shipbuilding, balloon and airship design, and provide educational resources for further exploration.

### 00:00:00

In this part of the video, the narrator explores why a transatlantic ship floats while a coin sinks, using Archimedes’ Principle. It begins with a comparison between the weights of a ship and a coin, explaining the ship floats due to Archimedes’ Principle. The principle, originating over 2,200 years ago, is illustrated through the story of how Archimedes discovered it. King Hiero II of Syracuse suspected his gold crown was adulterated, and Archimedes theorized he could verify the purity if he could measure its volume. Inspired when he observed water displacement in his bath, Archimedes realized that an object displaces an amount of water equivalent to its volume. This principle allowed him to determine the crown’s density and composition.

### 00:03:00

In this segment of the video, the explanation pertains to Archimedes’ principle and its applications. It describes how to determine the volume of an object, such as a crown, by immersing it in water and measuring the displaced water volume. The segment recounts the legend of Archimedes discovering that a goldsmith deceived a monarch. Archimedes noted that an object in a fluid experiences an upward force equal to the weight of the fluid it displaces, a principle termed buoyancy. The segment further explains density and provides examples of objects floating in different fluids due to their densities. It concludes with a formula for Archimedes’ principle and a practical example demonstrated by the Math2Me channel, illustrating how to calculate the thrust force on a submerged cube to determine if it will float or sink.

### 00:06:00

In this part of the video, the presenters, José and Kukis, discuss the buoyancy of a cube to determine whether it will sink or float. They calculate the volume of the cube to be 0.008 cubic meters and figure out the upward thrust as 78.48 newtons. Since the cube weighs 57 kilos and its weight in newtons is much greater than the thrust, it will sink. They explain that according to Archimedes’ principle, an object will sink if its weight in the fluid is positive, otherwise, it will float. They then demonstrate an experiment where a ball of plasticine, which normally sinks, can be made to float by reshaping it into a bowl, which increases the volume and displaces more water, creating enough thrust to keep it afloat.

### 00:09:00

In this part of the video, the speaker explains why objects like boats float by discussing the relationship between density and buoyancy. They clarify that if combined with air, the overall density of an object can be less than water, enabling it to stay afloat. The concept is likened to a boat that remains buoyant because its shape allows it to hold a large volume of air, displacing water and generating upward thrust. The principle derived from Archimedes is crucial for various applications, including shipbuilding, balloon and airship design, and the operation of densimeters. This principle also allows submarines and fish to move up and down in water. Further, the segment includes a thank you to Alex Andalón from the Math2Me Channel for his mathematical advice and promotes additional educational resources from Platzi, along with calls to action to like, share, and subscribe to the channel.