Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Linked equation: ρ = m/V
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Aim
To measure the density of regular and irregular solid objects and of a liquid.
Method
- Regular solid: measure the length, width and height with a ruler and calculate the volume. Measure the mass on a balance.
- Irregular solid: fill a displacement (eureka) can until water runs out of the spout. Put a measuring cylinder under the spout and gently lower the object in. The volume of water collected = the volume of the object. Measure the mass on a balance.
- Liquid: put a measuring cylinder on a balance and zero it. Pour in a known volume of liquid and record the mass.
- Calculate density: ρ = m ÷ V.
| Measurements | Mass (balance); volume (ruler or measuring cylinder) |
| Calculated | Density = mass ÷ volume |
| Units | g/cm³ or kg/m³ (1 g/cm³ = 1000 kg/m³) |
Questions
Q1 (F) Describe how to find the density of a regular block.
Show answer
Measure the length, width and height with a ruler; volume = length × width × height. Measure the mass on a balance. Density = mass ÷ volume.
Q2 (F) A block measures 5.0 cm × 4.0 cm × 2.0 cm and has a mass of 108 g. Calculate its density in g/cm³.
Show answer
Volume = 5.0 × 4.0 × 2.0 = 40 cm³
F: ρ = m / V
I: ρ = 108 ÷ 40
A: 2.7 g/cm³
Q3 (F) Describe how to find the volume of an irregular stone.
Show answer
Fill a displacement can with water up to the spout. Place a measuring cylinder under the spout and gently lower in the stone. The volume of water that flows into the cylinder equals the volume of the stone.
Q4 (F) How should you read the volume on a measuring cylinder?
Show answer
With your eye level with the surface of the water, reading from the bottom of the meniscus.
Q5 (F/H) A 150 g stone displaces 60 cm³ of water. Calculate its density in g/cm³ and in kg/m³.
Show answer
ρ = m ÷ V = 150 ÷ 60 = 2.5 g/cm³
× 1000 = 2500 kg/m³
Q6 (F/H) An empty measuring cylinder has a mass of 80 g. With 50 cm³ of oil in it, the mass is 120 g. Calculate the density of the oil in kg/m³.
Show answer
Mass of oil = 120 − 80 = 40 g
ρ = 40 ÷ 50 = 0.80 g/cm³
× 1000 = 800 kg/m³
Q7 (F/H) Give one source of error when using a displacement can, and how to reduce it.
Show answer
E.g. water splashes out when the object is dropped in – lower it gently on a thread. Or water is still dripping from the spout – wait until it stops before reading the cylinder.
Q8 (H) Explain why a density of 2.7 g/cm³ is the same as 2700 kg/m³.
Show answer
1 g = 1 × 10−3 kg and 1 cm³ = 1 × 10−6 m³.
So 1 g/cm³ = 10−3 ÷ 10−6 = 1000 kg/m³, and 2.7 g/cm³ = 2.7 × 1000 = 2700 kg/m³.
