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Density is a measure of how much mass is contained in a given volume. In simpler terms, it tells us how tightly packed the material's matter is. To find the density of a material, we need to know its mass and the space it occupies. This concept is essential in understanding buoyancy and other physical phenomena.
In the context of the given problem, density is calculated using the formula:

• Density, \( \rho = \frac{\text{Weight in air}}{\text{Volume}} \)

Here, the weight in air is given as 300 N, but since we want to find the mass, it is important to remember that weight is the force due to gravity on the mass. In formula terms, \( \, \text{Weight} = \text{mass} \times g \, \) where \( g \) is gravity (approximated to \( 9.8 \, \text{m/s}^2 \)). Therefore, to solve for density, we will use the volume obtained in the problem's step-by-step solution.
By substituting the volume calculated into the equation above, we can solve for the density, giving us a clearer picture of the material's mass per unit volume.

The calculation of volume involves determining the amount of space an object occupies. In fluid displacement methods, volume is directly related to buoyant force. This is insightful for determining factors such as the material's weight when submerged in a fluid.
In the exercise, the volume of the material is calculated based on the buoyant force when it is immersed in alcohol. According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced by the object. This leads us to the formula:

• Buoyant Force, \( F = \rho_{\text{fluid}} \times g \times V \)

Given that the density of alcohol is \( \rho = 0.700 \times 1000kg/m^3 \), the buoyant force is 100 N, and using the value of gravity \( g = 9.8 \text{m/s}^2 \), volume \( V \) is calculated by rearranging the formula as follows:
\( V = \frac{F}{\rho \times g} \). This calculation allows us to find the volume of the unknown material easily, given its buoyant force.

Specific gravity is a dimensionless quantity that indicates the ratio of the density of a substance to the density of a reference substance, typically water. This concept is advantageous as it compares the density of the object without requiring units, making it a versatile tool in fluid mechanics.
In the exercise, specific gravity plays a crucial role in understanding the context of immersion. The specific gravity of the alcohol is given as 0.700, meaning the alcohol's density is 70% that of water, taken at approximately \( 1000 \, kg/m^3 \). This relation can be expressed mathematically as:

• \( \text{Specific Gravity} = \frac{\text{Density of substance}}{\text{Density of water}} \)

Because the difference in the object's weight between air and alcohol accounts for this specific context, the specific gravity helps establish the density needed to solve for both volume and buoyant force. By understanding and using specific gravity, students can effectively grasp the changes in buoyant behavior when an object is submerged in various fluids.