What is the relationship between upthrust and weight for floating objects?

For floating objects, upthrust equals the weight of the object.

When an object floats in a fluid, such as water, it experiences an upward force called upthrust or buoyant force. This force is a result of the pressure exerted by the fluid on the object. According to Archimedes' principle, the upthrust acting on an object is equal to the weight of the fluid displaced by the object. For an object to float, the upthrust must balance the weight of the object. This means that the weight of the object is exactly equal to the upthrust.

Imagine you have a boat floating on a lake. The boat pushes water out of the way, creating a space where the boat sits. The water that has been pushed aside exerts an upward force on the boat. If the boat's weight is 500 newtons, the upthrust must also be 500 newtons for the boat to float. If the upthrust were less than the boat's weight, the boat would sink until the upthrust increased to match the weight.

This balance of forces is why objects with a density less than the fluid they are in will float. Density is mass per unit volume, and if an object is less dense than the fluid, it means it will displace a volume of fluid equal to its own weight before it is completely submerged. For example, a piece of wood floats on water because wood is less dense than water. The wood displaces enough water to create an upthrust equal to its weight before it is fully submerged.

Understanding the relationship between upthrust and weight helps explain why some objects float while others sink, and it is a fundamental concept in fluid mechanics and buoyancy.