Buoyant Force Calculation: A Submerged Wood Cylinder

Summary

This educational video walks viewers through the concept of buoyant force using a practical example of a wooden cylinder submerged in water. It demonstrates the steps of calculating the buoyant force, from converting units to applying the buoyant force equation. Key concepts such as the importance of using the fluid's density and understanding volume displacement are discussed. The video also includes an experimental demonstration with a force sensor, showing how the measured force correlates with the calculated buoyant force. Common student mistakes are highlighted to ensure better understanding of this principle in physics.

Takeaways

• 😀 The buoyant force acts on submerged objects in a fluid.
• 😀 The diameter and height of the wood cylinder are given, with conversions needed to work in meters.
• 😀 The volume of the cylinder can be calculated using the formula for the volume of a cylinder: π × radius² × height.
• 😀 The buoyant force is determined by the weight of the fluid displaced by the object.
• 😀 The density of the fluid displaced by the object, not the density of the object itself, is used in the buoyant force equation.
• 😀 The volume of fluid displaced by the object equals the volume of the object when it is fully submerged.
• 😀 For floating objects, the volume of the fluid displaced is less than the volume of the object itself.
• 😀 The density equation (Density = mass/volume) is used to find mass from the given density and volume of fluid displaced.
• 😀 The gravitational force acting on the object can be calculated from its mass and the gravitational field strength.
• 😀 Measurements made using a force sensor help verify the calculated buoyant force, but what is measured is the downward applied force to keep the object submerged, not the buoyant force itself.
• 😀 Two common mistakes when solving for buoyant force are using the wrong density (the density of the object vs. the fluid) and misunderstanding the volume of fluid displaced when the object is partially submerged.

Q & A

What is the buoyant force acting on a submerged object?

The buoyant force is the upward force exerted by a fluid that opposes the weight of an object submerged in the fluid.

Why do we need to convert the diameter of the wood cylinder to meters?

The densities of the wood and water are given in kilograms per cubic meter, so converting the diameter and other measurements to meters ensures that the units are consistent for the calculations.

How is the radius of the wood cylinder calculated?

The radius is calculated by dividing the diameter of the cylinder by 2. In this case, the diameter is 0.0507 meters, so the radius is 0.02535 meters.

Why is the volume of the displaced fluid the same as the volume of the submerged object?

When an object is fully submerged in a fluid, it displaces an amount of fluid equal in volume to the volume of the object itself.

What is the formula for calculating the volume of a cylinder?

The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.

What is the mistake made when calculating the buoyant force?

The mistake was using the density of the wood (the object) instead of the density of water (the fluid displaced by the object) in the buoyant force equation.

How is the correct buoyant force calculated?

The buoyant force is calculated by using the formula: Buoyant Force = Density of displaced fluid × Volume of displaced fluid × Gravitational field strength. After correcting the mistake, the buoyant force was found to be approximately 1.7 newtons.

What was measured during the experiment, and what did the results show?

The experiment measured the downward applied force required to hold the wood cylinder submerged in the water. The measured force was about 0.80–0.81 newtons, which was close to the calculated buoyant force of 0.79 newtons.

What is the significance of the free-body diagram in solving for forces acting on the wood cylinder?

The free-body diagram helps visualize all the forces acting on the object (buoyant force, force of gravity, and applied force) and allows for the correct sum of forces to solve for the unknown forces.

What two common mistakes do students make when working with the buoyant force equation?

The two common mistakes are: 1) Confusing the density of the object with the density of the fluid displaced, and 2) Not recognizing that the volume in the buoyant force equation refers to the volume of the displaced fluid, which is equal to the volume of the object when fully submerged.