An object floats in a fluid when its average density is less than the fluid’s density. When it floats at rest, upthrust equals weight. These are two models of the same situation, and a good answer uses whichever the question needs.
This lesson belongs to mass, weight and density. It uses the density work from calculating an unknown volume and the idea of balanced forces from forces and momentum.
Which model should you use?
Density comparison answers “will it float or sink?” quickly. Compare the object’s average density with the fluid’s. Less dense floats, more dense sinks, and equal density stays where it is placed.
Force balance explains what happens at the surface. Two forces act on a floating object: weight downwards and upthrust upwards. At rest they are equal. Upthrust is the force from the fluid, equal to the weight of the fluid the object displaces.
Step by step
- Choose the model from the wording of the question.
- For density: calculate ρ = m/V for the object with matching units, then compare with the fluid.
- For forces: name both forces and their directions, then say whether they are equal or unequal.
- State the conclusion in a full sentence that refers to the numbers.
Worked example
A wooden block has mass 0.60 kg and volume 1000 cm³. Water has density 1000 kg/m³. Take g = 10 N/kg.
Explain whether the block floats, and find how much of it is under the water. (Invented data.)
Step 1, density: V = 1000 cm³ = 0.001 m³. ρ = 0.60 ÷ 0.001 = 600 kg/m³.
Step 2, compare: 600 kg/m³ is less than 1000 kg/m³, so the block floats.
Step 3, forces: weight = mg = 0.60 × 10 = 6.0 N. At rest, upthrust = 6.0 N.
Step 4, displaced water: upthrust equals the weight of water displaced, so the displaced water weighs 6.0 N and has mass 0.60 kg.
Step 5, volume under water: V = 0.60 ÷ 1000 = 0.000 6 m³ = 600 cm³, which is 60% of the block.
Check: 600 kg/m³ ÷ 1000 kg/m³ = 0.6, matching 60%. The density route and the force route agree.
The mistake to watch for
Mistaken answer: “The block floats because it is light.”
Lightness alone does not decide it. A light pebble sinks and a heavy ship floats.
The correction is to compare densities, using numbers: “The block’s density is 600 kg/m³, which is less than water’s 1000 kg/m³, so it floats.” A second slip is saying upthrust is greater than weight for a floating object. At rest they are equal.
Check yourself
1. An object has mass 0.30 kg and volume 400 cm³. Does it float in water (1.0 g/cm³)?
Show answer
Density = 300 g ÷ 400 cm³ = 0.75 g/cm³. This is less than 1.0 g/cm³, so it floats.
2. An object of mass 2.0 kg has a volume of 500 cm³. Will it float in water? Give the density.
Show answer
2000 g ÷ 500 cm³ = 4.0 g/cm³ (4000 kg/m³). This is greater than water, so it sinks.
3. A boat floats at rest and has a weight of 8000 N. What is the upthrust on it? Explain.
Show answer
8000 N. The boat is at rest, so the forces are balanced: upthrust equals weight.
Where this leads next
Next, practise judging whether a calculated density could be real in identifying an unreasonable material-density answer. Pressure in liquids, which builds on these ideas, is in pressure in solids and fluids.
Good floating explanations combine a number, a comparison and a sentence. A teacher can help you build that habit through online one-to-one Physics tuition.