91Ó°ÊÓ

The concept of buoyant force is rooted deeply in Archimedes’ Principle, which states that any object fully or partially submerged in a fluid experiences an upward force, or buoyant force, equal to the weight of the fluid displaced by the object. In simpler terms, when you put something in water, it pushes water out of the way and, in turn, the water pushes back against the object, trying to float it.

In our exercise, the ore sample weighed 17.50 N in air and the tension in the cord was 11.20 N when immersed in water. The buoyant force is the difference between these two weights.

• Weight in air: 17.50 N
• Weight in water: 11.20 N
• Buoyant Force: 6.30 N

The buoyant force here is calculated as: \( F_b = 17.50 \, \mathrm{N} - 11.20 \, \mathrm{N} = 6.30 \, \mathrm{N} \).

This force represents the weight of the water displaced by the sample, which is key to determining the next steps: calculating the volume and density of the sample.

Density is a measure of how much mass is packed into a unit volume of a substance. It's calculated by dividing the mass by the volume: \( \rho = \frac{\text{mass}}{\text{volume}} \). Understanding this allows us to figure out how tightly packed the atoms or molecules are within an object.

To find the density of the ore sample, we first need its mass. We can calculate the sample’s mass by dividing the weight in air by the gravitational acceleration: \( m = \frac{17.50 \, \mathrm{N}}{9.8 \, \mathrm{m/s^2}} \approx 1.7857 \, \mathrm{kg} \).

With mass and volume determined, the density calculation becomes straightforward.

• Density \( \rho = \frac{1.7857 \, \mathrm{kg}}{0.000643 \, \mathrm{m^3}} \approx 2777 \, \mathrm{kg/m^3} \)

The calculated density helps in understanding the composition and identification of the material, as each substance has a characteristic density.

Determining the volume of an object using Archimedes' Principle involves understanding how much water is displaced when the object is submerged. This displaced water is directly correlated to the volume of the object itself, since the buoyant force equals the weight of the displaced water.

The formula relates these concepts: \( F_b = V \times \rho_{water} \times g \), where \( V \) is the volume, \( \rho_{water} \) is the density of water, and \( g \) is the acceleration due to gravity.

Rearranging to solve for \( V \), we have:

• \( V = \frac{F_b}{\rho_{water} \times g} = \frac{6.30 \, \mathrm{N}}{1000 \, \mathrm{kg/m^3} \times 9.8 \, \mathrm{m/s^2}} \approx 0.000643 \, \mathrm{m^3} \)

This volume reflects how much space the ore sample takes up, key in helping us calculate its density. Knowing the volume is crucial for understanding an object's physical properties, applicable in real-world scenarios like material science and engineering.