How Do You Calculate Density Using Displacement?

You calculate density using displacement by determining the volume of an irregularly shaped object through water displacement, then dividing its mass by that volume.

Here's a step-by-step breakdown:

1. Measure the Mass: Determine the mass (m) of the object using a balance or scale. Record this value in grams (g) or kilograms (kg).

2. Prepare a Displacement Container: A displacement tank (overflow can) works best. Alternatively, a graduated cylinder large enough to fully submerge the object will also work.

3. Fill and Prepare the Container:

   • Displacement Tank: Fill the displacement tank with water until it just starts to overflow. Allow the excess water to drain completely. Place a small beaker or container beneath the spout to collect the displaced water.
   • Graduated Cylinder: Record the initial volume of water in the graduated cylinder (V₁). Ensure the water level is high enough to allow for full submersion of the object.

4. Submerge the Object: Carefully lower the object into the displacement tank or graduated cylinder. Ensure the object is fully submerged and doesn't touch the sides of the container.

5. Collect Displaced Water (Displacement Tank) or Note the New Volume (Graduated Cylinder):

   • Displacement Tank: Collect all the water that overflows from the tank into the beaker. This water represents the volume of the object.
   • Graduated Cylinder: Note the new volume reading on the graduated cylinder (V₂).

6. Measure the Volume of Displaced Water:

   • Displacement Tank: Pour the water collected in the beaker into a graduated cylinder and measure the volume (V) of the displaced water. Record this value in milliliters (mL) or cubic centimeters (cm³), as 1 mL = 1 cm³.
   • Graduated Cylinder: Calculate the volume of displaced water by subtracting the initial volume (V₁) from the final volume (V₂): V = V₂ - V₁.

7. Calculate Density: Density (ρ) is calculated by dividing the mass (m) of the object by its volume (V):

   ρ = m / V

   Where:

   • ρ = density (typically in g/cm³ or kg/m³)
   • m = mass of the object (typically in grams or kilograms)
   • V = volume of the object (which is the volume of the displaced water, typically in cm³ or m³)

Example:

Let's say you have a rock with a mass of 50g. You use a displacement tank and collect 20 mL of water when the rock is submerged.

• m = 50 g
• V = 20 mL = 20 cm³

Therefore, the density of the rock is:

ρ = 50 g / 20 cm³ = 2.5 g/cm³

Key Considerations:

• Air Bubbles: Ensure there are no air bubbles trapped on the object when submerged, as this will affect the accuracy of the volume measurement.
• Accuracy of Measurement: The accuracy of your density calculation depends on the accuracy of your mass and volume measurements. Use precise instruments for best results.
• Water Temperature: Water density changes slightly with temperature. For extremely precise measurements, account for water temperature.