A metal object weighs. 26.0 g in air and 21.48 g when totally immersed in
water. What is the volume of the object? Its mass density?
To find the volume of the metal object, we can use Archimedes' principle which states that the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
First, let's calculate the weight of the metal object in air. Given that it weighs 26.0 g, we can convert it to its weight in Newtons using the acceleration due to gravity (9.8 m/s²):
Weight in air = mass × acceleration due to gravity
Weight in air = (26.0 g) × (9.8 m/s²) = 0.2548 N
Next, let's calculate the weight of the fluid displaced by the object when it is submerged in water. This weight difference is equal to the buoyant force acting on the object. Given that it weighs 21.48 g when immersed in water, we can convert it to its weight in Newtons:
Weight in water = mass × acceleration due to gravity
Weight in water = (21.48 g) × (9.8 m/s²) = 0.210504 N
Now, we can find the weight difference when the object is submerged:
Weight difference = Weight in air - Weight in water
Weight difference = 0.2548 N - 0.210504 N = 0.044296 N
According to Archimedes' principle, this weight difference is equal to the weight of the fluid displaced, which is also equal to the buoyant force acting on the object.
Thus, the volume of the metal object can be calculated using the formula:
Volume = Weight difference / (density of water × acceleration due to gravity)
The density of water is typically around 1000 kg/m³, but it can vary slightly depending on temperature and impurities.
Assuming a density of 1000 kg/m³, we can plug the values into the formula:
Volume = 0.044296 N / (1000 kg/m³ × 9.8 m/s²)
Calculating this gives us the volume of the metal object.
To find the mass density of the object, we need to divide the mass of the object by its volume:
Mass density = mass / volume
Plugging the given mass of the object (26.0 g) into the formula, along with the calculated volume, will give us the mass density.