How to Calculate Buoyant Force When Object Is Immersed in Water?

The buoyant force acting on an object fully or partially immersed in water is precisely equal to the weight of the water it displaces.

Understanding Buoyant Force: Archimedes' Principle

Buoyant force is the upward force exerted by a fluid that opposes the weight of an immersed object. This fundamental concept is described by Archimedes' Principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

As stated in the reference, "This weight is supported by the surrounding fluid, so the buoyant force must equal wfl, the weight of the fluid displaced by the object. FB=wfl, where FB is the buoyant force and wfl is the weight of the fluid displaced by the object." This means to calculate the buoyant force (FB), you simply need to determine the weight of the water pushed aside by the object.

Steps to Calculate Buoyant Force (FB)

To calculate the buoyant force when an object is immersed in water, follow these steps:

1. Determine the Volume of Displaced Water (Vfl):

   • If the object is fully submerged, the volume of displaced water is equal to the object's total volume (Vobj).
   • If the object is partially submerged (floating), the volume of displaced water is equal to the volume of the object that is submerged below the waterline.

2. Identify the Density of Water (ρfl):

   • The density of fresh water is approximately 1000 kg/m³ (or 1 g/cm³).
   • For saltwater, the density is slightly higher, around 1025 kg/m³.

3. Calculate the Mass of Displaced Water (mfl):

   • Use the formula: mfl = ρfl × Vfl
     • Where mfl is the mass of the displaced fluid, ρfl is the density of the fluid, and Vfl is the volume of the displaced fluid.

4. Calculate the Weight of Displaced Water (wfl):

   • Use the formula: wfl = mfl × g
     • Where g is the acceleration due to gravity, approximately 9.81 m/s² on Earth.

5. Confirm Buoyant Force (FB):

   • According to Archimedes' Principle and the provided reference, FB = wfl. Therefore, the calculated weight of the displaced water is your buoyant force.

Simplified Formula:
Combining these steps, the buoyant force can be directly calculated using the formula:
FB = ρfl × Vfl × g

Key Variables for Buoyant Force Calculation

To make the calculation clear, here are the variables involved:

Practical Example: Submerged Object

Let's consider a practical scenario to illustrate the calculation.

Scenario: A solid metal cube with sides of 0.2 meters is fully submerged in fresh water.

Given:

• Side length of cube (L) = 0.2 m
• Density of fresh water (ρfl) = 1000 kg/m³
• Acceleration due to gravity (g) = 9.81 m/s²

Calculation Steps:

1. Calculate the Volume of the Cube (Vobj):

   • Since the cube is fully submerged, Vfl = Vobj.
   • Vobj = L³ = (0.2 m)³ = 0.008 m³
   • So, Vfl = 0.008 m³

2. Calculate the Mass of Displaced Water (mfl):

   • mfl = ρfl × Vfl = 1000 kg/m³ × 0.008 m³ = 8 kg

3. Calculate the Weight of Displaced Water (wfl):

   • wfl = mfl × g = 8 kg × 9.81 m/s² = 78.48 N

4. Determine Buoyant Force (FB):

   • FB = wfl = 78.48 N

Therefore, the buoyant force acting on the fully submerged metal cube is 78.48 Newtons.

Factors Influencing Buoyant Force

The buoyant force primarily depends on:

• Volume of the Object Submerged: The more volume of an object that is submerged in the fluid, the greater the volume of fluid displaced, and thus the greater the buoyant force.
• Density of the Fluid: Denser fluids (like saltwater compared to fresh water) will exert a greater buoyant force for the same volume of displacement because the displaced fluid will weigh more.
• Gravity: The local gravitational acceleration also affects the weight of the displaced fluid, though this is usually considered constant for practical purposes on Earth.

It is important to note that the density or weight of the object itself does not directly affect the buoyant force. Instead, the object's density determines whether it sinks (object denser than fluid), floats (object less dense than fluid), or is neutrally buoyant (object density equals fluid density).