Density Notes

Density

  • Density is represented by the Greek letter 'rho' (\rho).

  • Density is defined as mass per unit volume: \rho = \frac{m}{V}

    • m = mass, typically in grams (g)

    • V = volume, typically in cubic centimeters (cm³)

    • \rho = density, typically in g/cm³

  • Example:

    • If \rho = 8 \frac{g}{cm^3}, then mass can be calculated as m = \rho \times V

Density of Water

  • Density of water is approximately 1 \frac{g}{cm^3}.

  • Conversion: 1 \frac{g}{cm^3} = 1000 \frac{kg}{m^3}

Finding Density of Regular Shapes

  • Measure Volume: Use a ruler.

    • For a rectangular shape: V = a \times b \times c (where a, b, and c are the dimensions)

    • For a cylindrical shape: V = A \times l = \pi r^2 \times l (where A is the area of the base, l is the length/height, and r is the radius). Measure diameter to find radius (r = d/2).

    • Area of circle: A = \pi r^2

  • Measure Mass: Use an electronic balance (not scales!).

  • Accuracy Considerations:

    • Zero the balance before measuring.

    • Ensure the surface is level.

  • Calculate Density: \rho = \frac{m}{V}

Density of Irregular Shapes

  • Use the displacement method with water.

Small Irregular Shapes

  1. Measure the mass using a balance.

  2. Measure the initial volume of water in a measuring cylinder.

    • Read the volume at eye level, at the bottom of the meniscus.

  3. Carefully insert the shape into the measuring cylinder to avoid spillage.

    • Ensure the shape is fully submerged.

  4. Measure the new volume.

  5. Calculate the volume of the shape by subtracting the initial volume from the new volume: V{shape} = V{new} - V_{initial}

  6. Calculate Density: \rho = \frac{m}{V}

Big Irregular Shapes

  1. Measure Mass: Level balance zeroed

  2. Use a Eureka can (displacement can):

    • Fill the Eureka can with water until it reaches the spout/hole.

    • Place the shape in the can, ensuring it is fully submerged, which will cause water to be displaced and spill out.

    • Collect the displaced water in a beaker.

  3. Measuring Volume of Displaced Water

    • Using a measuring cylinder, measure the volume of the displaced water and record it in cm³

    • Level of eye should be the same as the meniscus

  4. Calculate Density: \rho = \frac{m}{V}

Density of Liquids

  1. Measure Mass:

    • Zero the balance.

    • Pour the liquid into the measuring container.

    • Measure the mass of the liquid using the balance.

  2. Measure Volume:

    • Read the volume of the liquid at eye level in the measuring cylinder.

  3. Calculate Density: \rho = \frac{m}{V}