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When an object is submerged in a fluid, such as a glass ball in milk, it experiences an upward force called the buoyant force. This force is a result of the pressure difference at different depths of the fluid. According to Archimedes' Principle, the buoyant force is equal to the weight of the fluid that the object displaces once submerged.
Understanding this concept helps explain why some objects float while others sink. For the glass ball, the buoyant force can be calculated by multiplying the displaced fluid's volume, its density, and the gravitational acceleration.

• Volume of displaced fluid: You need to know the volume of the object submerged, here it’s the volume of the glass ball.
• Density of the fluid: Look at the fluid in which the object is submerged (e.g., milk with density of 1.03 g/cm³).
• Gravitational acceleration: Typically, this is approximately 9.8 m/s² on Earth's surface.

Adding these up provides the magnitude of the buoyant force in newtons.

Density is a key concept when analyzing the interaction between an object and a fluid. It is defined as the mass per unit volume of a substance. In our example of the glass ball in milk, density explains how much mass of milk occupies a given volume. A fluid's density directly affects the buoyant force experienced by a submerged object.
If a fluid is denser, it will exert a stronger buoyant force as it can support more weight over the same volume. Therefore, knowing the milk's density is crucial for calculating the buoyant force acting on the submerged glass ball. The formula for density is given by

• Density (\(\rho \)) = Mass/Volume

This is critical when comparing the immersive behavior of objects in different fluids.

Newton's Third Law states that for every action, there is an equal and opposite reaction. In the context of our topic, when the glass ball exerts a force downward on the milk (due to gravity), the milk exerts an equal force upward, which includes the normal force and the buoyant force.
This upward force counteracts the weight of the ball, making it seem less heavy, and this perceived weight is called the apparent weight. Therefore, understanding Newton's Third Law is important when calculating the forces acting on submerged objects and helps us determine:

• Apparent weight (\( W' \)) of the object
• The actual weight (\( W \)) minus the buoyant force (\( F_b \))

These insights are essential for calculating the normal force the container's surface feels from the ball.

The volume of a sphere is an important geometric formula that is essential when dealing with objects submerged in a fluid. It allows us to determine the extent of fluid displaced by the object, which in turn is used to calculate the buoyant force. The formula for the volume (\( V \)) of a sphere is:

• \[ V = \frac{4}{3} \pi r^3 \]

This equation shows us that the volume of a sphere depends on its radius raised to the third power, multiplied by a constant (\( \frac{4}{3} \pi \)).
For the glass ball example, using the radius of 2.00 cm, we can calculate its exact volume, which is crucial for further buoyancy and force calculations—it tells us how much space the sphere takes up in the milk.