Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 1.6000kg when weighed in air.
To calculate the true mass of the aluminum piece in vacuum, we need to consider the buoyant force acting on the object in air.
When an object is submerged or immersed in a fluid (in this case, air), it experiences an upward force called buoyant force. According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced by the object.
To find the true mass of the aluminum piece, we'll follow these steps:
Step 1: Determine the buoyant force.
- The buoyant force (Fb) is given by the formula: Fb = ρ * V * g
- Where ρ is the density of air (approximately 1.2 kg/m³),
- V is the volume of the aluminum piece, and
- g is the acceleration due to gravity (approximately 9.8 m/s²).
Step 2: Calculate the weight in air.
- The weight in air (Wa) is calculated using the formula: Wa = m * g
- Where m is the apparent mass of the aluminum piece (1.6000 kg),
- and g is the acceleration due to gravity (9.8 m/s²).
Step 3: Determine the true mass.
- The true mass (m_true) is given by the formula: m_true = m_apparent - (Fb / g)
- Where m_apparent is the apparent mass (1.6000 kg),
- Fb is the buoyant force calculated in Step 1, and
- g is the acceleration due to gravity (9.8 m/s²).
Let's calculate the true mass of the aluminum piece:
Step 1: Calculate the buoyant force.
Fb = ρ * V * g
= 1.2 kg/m³ * V * 9.8 m/s²
Step 2: Calculate the weight in air.
Wa = m * g
= 1.6000 kg * 9.8 m/s²
Step 3: Determine the true mass.
m_true = m_apparent - (Fb / g)
= 1.6000 kg - (1.2 kg/m³ * V * 9.8 m/s²) / 9.8 m/s²
To find the true mass, we need the volume of the aluminum piece. Please provide the volume, and I'll calculate the true mass for you.