What is the density of the bracelet when a bracelet weighing 383 g in air is submerged in water, and a scale measures a weight of 349 g? Is the bracelet made of pure gold based on the calculated density?
To find the density of the bracelet, divide its mass by its volume. The density of the bracelet is 10,969.92 g/cm³. Since the density of pure gold is 19.3 g/cm³, the bracelet is not made of pure gold.
Calculating Density:
Density is defined as mass per unit volume. In this scenario, we need to calculate the density of a bracelet that weighs 383 g in air and 349 g in water. The difference in weight when the bracelet is submerged in water is due to the buoyant force of the water pushing up on the bracelet.
Using the formula density = mass / volume, we first determine the volume of the bracelet. The volume is calculated by dividing the weight in air by the density of water, which is 1.00 g/cm³. This gives us a volume of 0.0349 cm³.
Next, we calculate the density of the bracelet by dividing the mass by the volume: 383 g / 0.0349 cm³ = 10,969.92 g/cm³. This is the density of the bracelet when submerged in water.
Since the density of pure gold is 19.3 g/cm³, we can conclude that the bracelet is not made of pure gold based on the calculated density.
In summary, the bracelet has a density of 10,969.92 g/cm³, indicating that it is made of a material other than pure gold. The difference in density helps us determine the composition of the bracelet when submerged in water.