6.6. Buoyant Force and Archimedes’ Principle

The buoyant force is the upward force exerted by a fluid on an object placed in it. This force is equal to the weight of the fluid displaced by the object.

The concept of buoyant force refers to the upward force that a fluid exerts on an object that is submerged in it. This force acts in the opposite direction to gravity. For instance, if you place a ball in water, the water will push the ball upwards with a force that equals the weight of the water that the ball displaces. This means that the size and shape of the object affect how much fluid it displaces while submerged in the fluid.

Imagine you have a beach ball and you push it underwater. You will feel the ball pushing back against your hands. This push is the buoyant force, equal to the weight of the water you have displaced by pushing the ball down.

The magnitude of the buoyant force is given by: Fb=ρ⋅V⋅g Where: ○ Fb = Buoyant force (N) ○ ρ = Density of the fluid (kg/m³) ○ V = Volume of the fluid displaced (m³) ○ g = Gravitational acceleration (9.8 m/s²)

The magnitude of the buoyant force can be calculated using the formula: Fb = ρ ⋅ V ⋅ g. Here, ρ represents the density of the fluid where the object is submerged, V is the volume of fluid that the object displaces, and g is the acceleration due to gravity. This means that if you know the density of the liquid and the volume of the object submerged, you can easily find the buoyant force acting on that object.

Think about a submerged basketball. If the basketball has a volume of 0.1 cubic meters and it's in water (which has a density of approximately 1000 kg/m³), the buoyant force can be found by using the formula. It shows how much water the basketball displaces and the upward force acting on it.

Archimedes' Principle states that: "Any object, completely or partially submerged in a fluid, experiences an upward buoyant force equal to the weight of the fluid displaced by the object."

Archimedes' Principle explains a fundamental property of fluids and buoyancy. It asserts that when an object is submerged in a fluid, it is pushed upwards by a force equal to the weight of the fluid that the object has displaced. This principle is pivotal in explaining why some objects float while others sink. It tells us that if the buoyant force is equal to or greater than the weight of the object, the object will float.

Consider a rubber duck floating in a bathtub. The duck displaces a certain amount of water equivalent to its weight, and the water pushes it upwards with a buoyant force. If the duck were heavier than the water it displaces, it would sink.

1. Ships and Submarines: Ships float because the buoyant force is greater than or equal to their weight. A submarine sinks or rises by controlling the amount of water in its ballast tanks to change its buoyancy.
2. Hot Air Balloons: Hot air balloons rise because the hot air inside the balloon is less dense than the surrounding cooler air, providing an upward buoyant force.

Archimedes’ Principle is applied in various real-world scenarios. For example, ships achieve buoyancy by displacing enough water to counterbalance their weight, hence they float. Submarines adjust their buoyancy by altering water in their tanks to dive or rise. Similarly, hot air balloons showcase buoyancy through the principle that hot air is less dense, enabling them to rise into the cooler surrounding air.

Think of a massive cargo ship floating on the sea. Even though it's heavy, it has a large hull that displaces a lot of water, creating enough buoyant force to keep it afloat. For hot air balloons, visualize a balloon rising into the sky because the heated air inside is lighter than the surrounding air, allowing it to ascend.

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