Measuring density with water displacement is a common technique used to find the volume of irregularly shaped objects, allowing you to calculate their density using the formula Density = Mass / Volume.
The Water Displacement Method
This method, based on Archimedes' principle, determines the volume of an object by measuring the volume of water it displaces.
Here's a step-by-step guide:
- Measure the Object's Mass: Use a scale to accurately determine the mass of the object you are measuring. Record this value (m).
- Prepare the Graduated Cylinder: Pour the water into the graduated cylindar to a certain initial volume. The cylinder should be large enough to hold the object and have clear volume markings. Record this initial water volume (V₁). Ensure the object will be fully submerged without overflowing the cylinder.
- Submerge the Object: Gently place the object into the graduated cylinder, ensuring it is fully submerged.
- Measure Final Volume: Note the new, higher water level in the cylinder. Record this final water volume (V₂).
- Calculate Displaced Volume: The difference between the final volume and the initial volume is the volume of the water displaced by the object. This displaced volume is equal to the volume of the object itself (V_object = V₂ - V₁). measure the amount of displaced water.
- Calculate Density: Now that you have the object's mass (m) and its volume (V_object), you can calculate the density. Divide mass by volume to determine density for each sample (D=m/V).
The Density Formula
The core of density calculation is the formula:
Density (D) = Mass (m) / Volume (V)
Using the water displacement method:
- Mass (m): Measured using a scale (e.g., in grams, g).
- Volume (V): Determined by the volume of displaced water (e.g., in milliliters, mL, or cubic centimeters, cm³). Since 1 mL = 1 cm³, these units are often interchangeable in this context.
The resulting density is typically expressed in units like grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³).
Example Calculation
Let's walk through an example:
- Suppose the mass of a small rock is 50.0 g.
- You pour the water into the graduated cylindar to an initial volume (V₁) of 100.0 mL.
- After placing the rock in the cylinder, the water level rises to a final volume (V₂) of 125.0 mL.
- Calculate Volume: The volume of the rock is the displaced volume:
V_rock = V₂ - V₁ = 125.0 mL - 100.0 mL = 25.0 mL. This is where you measure the amount of displaced water. - Calculate Density: Using the formula D=m/V:
D = 50.0 g / 25.0 mL = 2.0 g/mL.
So, the density of the rock is 2.0 g/mL.
Summary Table
Here's a quick look at the key measurements and calculation:
| Measurement/Calculation | Value | Units |
|---|---|---|
| Mass (m) | Sample Mass | Grams (g) |
| Initial Volume (V₁) | Water Level | Milliliters (mL) |
| Final Volume (V₂) | Water + Object Level | Milliliters (mL) |
| Object Volume (V) | V₂ - V₁ | Milliliters (mL) |
| Density (D) | m / V | g/mL or g/cm³ |
This method is simple and effective for finding the density of objects that sink in water and do not dissolve or react with water.
