Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 4.5000 kg when weighed in air.

To find the true mass of the aluminum piece in vacuum, we need to determine its actual mass without the effects of buoyancy caused by air.

The apparent mass of an object weighed in air includes the effect of buoyancy, which is caused by the displaced air. In order to calculate the true mass, we need to subtract the buoyant force from the apparent mass.

The buoyant force (B) experienced by the object can be determined using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.

In this case, the fluid being displaced is air, and we can assume that the density of air is constant at normal conditions (around 1.225 kg/m³).

To calculate the buoyant force, we can use the following formula:

B = ρ * V * g

Where:
- B is the buoyant force
- ρ (rho) is the density of the fluid (air)
- V is the volume of the object
- g is the acceleration due to gravity (9.8 m/s²)

Since the object is weighed in air, the weight measured in vacuum is equal to the apparent weight minus the buoyant force:

True mass = Apparent mass - Buoyant force

Now, let's calculate the buoyant force:

B = ρ * V * g
B = 1.225 kg/m³ * V * 9.8 m/s²

To find the volume (V) of the aluminum object, we need its density (ρ). The density of aluminum is approximately 2,700 kg/m³.

Now we have all the variables to calculate the true mass:

Buoyant force = 1.225 kg/m³ * V * 9.8 m/s²
True mass = Apparent mass - Buoyant force

To determine the true mass, we need the volume of the object. Could you please provide us with the volume or any other information about the object?