Final answer:
The formula for the density of a liquid using an object's actual and apparent mass can be expressed as rho_liquid = (m_object - m_apparent) / V_object, which simplifies to rho_liquid = rho_object since the volume of the object equals the volume of water displaced.
Step-by-step explanation:
To derive a formula for determining the density of a liquid using an object with known mass (m_object) and density (rho_object), you can perform a water displacement experiment to find the object's apparent mass when submerged (m_apparent). The difference between the object's actual mass and its apparent mass in water gives us the mass of the water displaced, which is equal to the volume of the object because the density of water is 1 g/mL. Therefore, the volume of the object (V_object) can be calculated using the equation V_object = m_object - m_apparent. The density of the liquid (rho_liquid) can be found using the formula rho_liquid = (m_object - m_apparent) / V_object, which is simplified to rho_liquid = rho_object since the volume of the object is equal to the volume of the water displaced.