Wait, What? An object can appear lighter in water without losing any mass.
When an immersed object experiences an upward buoyant force, a force meter can show a smaller apparent weight even though the object’s mass is unchanged. Density and buoyancy practicals are therefore excellent tests of whether students can separate mass, weight, volume and force instead of treating them as interchangeable.
Density starts with two independent measurements
Density is:
ρ = m/V
Mass usually comes from a balance. Volume may come from geometry for regular solids or liquid displacement for irregular ones. The final density inherits uncertainty from both measurements.
Regular solids: geometry can be the cleanest route
For a rectangular block, measure length, width and height and calculate V = lwh. For a cylinder, use V = πr²h. Choose calipers or a ruler according to the scale and required precision.
Small dimensional errors can matter strongly because some dimensions are squared or multiplied together. A diameter error in a cylinder affects the calculated cross-sectional area more than a simple linear reading might suggest.
Irregular solids: displacement measures occupied volume
If an object is fully immersed, the increase in water volume can estimate the object’s volume. A measuring cylinder works for suitable sizes; an overflow can is useful when the object is larger.
The Institute of Physics uses displacement-based density activities to make students measure mass and volume directly rather than treating density as a memorised formula. See IOPSpark density and buoyancy teaching resources.
Trapped air is a hidden volume error
Air bubbles stuck to an immersed object displace extra water, making the measured volume too large and the calculated density too low. Wetting the object carefully and checking for attached bubbles can matter more than reading another decimal place.
Meniscus and parallax still matter
Read liquid level at eye level using the correct part of the meniscus for the liquid and apparatus. If the initial and final readings are both biased by the same viewing angle, the displacement may still be distorted because the scale is not read geometrically correctly.
Buoyant force can be measured from force difference
If a force meter reads W in air and Wapp when the object is immersed:
buoyant force ≈ W − Wapp
For complete immersion in a fluid, Archimedes’ principle predicts that this upward force equals the weight of displaced fluid under suitable conditions.
Do not let the object touch the container
If the immersed object rests against the bottom or wall, the container supplies an additional contact force. The force meter no longer measures the simple tension expected in a freely suspended immersion experiment.
Quantitative window
An irregular object has mass 84.0 g. Water rises from 50.0 cm³ to 80.0 cm³ when the object is fully submerged.
V = 80.0 − 50.0 = 30.0 cm³
ρ = 84.0/30.0 = 2.80 g cm⁻³
If an air bubble made the apparent displaced volume 33.0 cm³, the calculated density would fall to about 2.55 g cm⁻³ even though the object itself had not changed.
Common misconceptions
- “Floating objects have no weight.” Their weight is balanced by upward forces.
- “Apparent weight loss means mass was lost.” Buoyant force changes the support force, not the object’s mass.
- “More displaced water always means higher density.” Displacement measures volume; density also depends on mass.
- “A very precise balance guarantees precise density.” Volume uncertainty may dominate.
Secondary → JC → deeper Physics
Secondary: measure mass and volume, calculate density, use displacement for irregular solids and observe buoyant-force effects.
JC: analyse uncertainty from multiple measurements, compare measured upthrust with displaced-fluid weight and distinguish density effects from fluid-force effects.
Deeper Physics: buoyancy extends to hydrostatics, compressibility, fluid-density gradients, stability, metrology and precision density measurement.
Checkpoint
A metal sample weighs 5.0 N in air and 4.2 N when fully immersed in water without touching the container.
- What is the measured buoyant force?
- Did the sample lose mass?
- What should happen if the same object is immersed in a denser liquid?
Answer key and WHY reasoning
The buoyant force is about 0.8 N. The sample did not lose mass; the liquid supplies an upward force that reduces the supporting tension. In a denser liquid, the buoyant force for the same displaced volume would generally be larger.
Authoritative next steps
- Institute of Physics: density and buoyancy resources
- Institute of Physics: measuring density of air
- SEAB O-Level syllabuses
Teaching Guide
Have students measure one object’s density by geometry and by displacement where possible, then compare the two. Ask which measurement dominates the uncertainty. For buoyancy, require a free-body diagram before any arithmetic so apparent weight is interpreted as a force balance rather than a mass change.