1.4 Density (3)
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1.
Define density in terms of mass and volume. State the formula relating density (ρ), mass (m), and volume (V).
Definition: Density is defined as the mass of an object divided by its volume.
Formula: ρ = m / V, where:
- ρ (rho) represents density (units: kg/m³ or g/cm³)
- m represents mass (units: kg or g)
- V represents volume (units: m³ or cm³)
2.
Question 1
Describe how to determine the density of a liquid, a regularly shaped solid and an irregularly shaped solid which sinks in a liquid, using the method of volume by displacement. Include appropriate calculations.
Determining the Density of a Liquid:
- Measure the mass of the liquid using a balance. Record this as 'm'.
- Measure the volume of the container used to hold the liquid. This can be done using a graduated cylinder. Record this as 'V'.
- Calculate the density using the formula: Density = Mass / Volume (ρ = m/V). Ensure the units are consistent (e.g., g/cm³).
Determining the Density of a Regularly Shaped Solid:
- Measure the mass of the solid using a balance. Record this as 'm'.
- Use calipers or a ruler to accurately measure the dimensions of the solid (length, width, height).
- Calculate the volume of the solid using the appropriate formula for its shape (e.g., Volume of a cube = lwh, Volume of a cuboid = lwh). Record this as 'V'.
- Calculate the density using the formula: Density = Mass / Volume (ρ = m/V). Ensure the units are consistent (e.g., g/cm³).
Determining the Density of an Irregularly Shaped Solid (Volume by Displacement):
- Fill a graduated cylinder partially with a known volume of liquid (e.g., water). Record this initial volume as 'V1'.
- Carefully lower the solid into the graduated cylinder, ensuring it is fully submerged and does not touch the sides.
- Record the new volume of the liquid in the cylinder as 'V2'.
- Calculate the volume of the solid by subtracting the initial volume from the final volume: Volume of solid = V2 - V1.
- Measure the mass of the solid using a balance. Record this as 'm'.
- Calculate the density using the formula: Density = Mass / Volume (ρ = m/V). Ensure the units are consistent (e.g., g/cm³).
3.
Explain, in terms of density, why a large ship made of steel floats on water, while a small steel block sinks. Consider the relationship between mass, volume, and density in your answer.
Ships are designed with a large volume, even though they are made of dense steel. This large volume results in a low average density for the ship (ρship). While the steel block has a high density (ρsteel), its volume is small. Therefore, the mass of the steel block (mblock = ρsteel * Vblock) is much greater than the buoyant force exerted by the water on the block.
A ship, however, displaces a volume of water equal to its own volume. The buoyant force on the ship is equal to the weight of the water displaced. Because the ship's volume is large, the buoyant force is large enough to support the ship's weight, even though the ship is made of a dense material. The average density of the ship is less than the density of water, allowing it to float. The steel block, with its small volume, displaces a much smaller volume of water, resulting in a buoyant force that is insufficient to support its weight, causing it to sink.