Floating and sinking

Drop a pebble into a pond and it vanishes to the bottom in an instant. Launch a steel ship loaded with thousands of tonnes of cargo into the same water and it glides calmly on the surface. Same kind of liquid, wildly different outcomes — so what decides the difference? Every object lowered into a liquid feels two forces pulling in opposite directions: its own weight pulling it down, and the liquid pushing back up on it with a buoyant force. Floating or sinking is nothing more than the outcome of that tug-of-war. This article builds the qualitative rule that settles it, shows how a simple spring-balance reading lets you measure the buoyant force directly, and explains — without any density formula — why a solid lump of steel sinks while the very same steel, shaped into a hollow ship, floats.

The core insight

An object sinks when its weight exceeds the buoyant force pushing up on it, and floats when the buoyant force rises to exactly balance its weight — which a spread-out or hollow shape achieves more easily than a compact one.

The core idea

Every object placed in a liquid experiences two forces at the same time, acting in opposite directions.

  • The gravitational force (weight) pulls the object downward, toward the centre of the Earth.
  • The buoyant force (upthrust), exerted by the liquid itself, pushes the object upward.

Whether the object floats or sinks depends purely on comparing the sizes of these two forces.

  • If the gravitational force is greater than the buoyant force, the downward pull wins and the object sinks.
  • If the buoyant force rises until it becomes equal to the gravitational force, the two forces balance, and the object floats — resting partly submerged and partly above the surface.

This comparison is the qualitative heart of Archimedes' Principle: an object immersed in a liquid, fully or partially, feels an upward force equal to the weight of the liquid it displaces. A floating object settles at just the depth where the liquid it pushes aside weighs exactly as much as the object itself — that is precisely why the buoyant force on a floating object equals its own weight. The buoyant force on a submerged object can be found directly with a spring balance, without ever calculating density:

Fbuoyant=Wair−WapparentF_{\text{buoyant}} = W_{\text{air}} - W_{\text{apparent}}

where: WairW_{\text{air}} is the weight shown on the spring balance when the object hangs in air, and WapparentW_{\text{apparent}} is the (smaller) reading once the object is fully lowered into the liquid. The liquid's push reduces the reading the balance shows, and that reduction is exactly the buoyant force. Shape is the hidden lever here. A solid, compact lump of steel pushes aside only a small volume of water for its weight, so the buoyant force on it stays small — smaller than its weight — and it sinks. The same steel, hammered into a hollow, spread-out hull, pushes aside a much larger volume of water before it is fully submerged. A larger displaced volume means a larger buoyant force, large enough to climb up and match the ship's weight while the hull is still mostly above the surface. Material alone never decides the outcome; shape, by controlling how much liquid gets displaced, does.

Figure
Two objects in water a compact steel ball resting on the bottom and a hollow steel hull floating on the surface with weight arrows down and buoyant force arrows up
Same steel, different shape — weight versus buoyant force compact steel ball hollow steel hull weight (large) buoyant force (small) weight greater than buoyant force — sinks weight buoyant force (large) forces equal — floats
Derivation AFinding the buoyant force with a spring balance

The goal of this reasoning is to show, using nothing beyond two spring-balance readings and simple subtraction, how the buoyant force on a submerged object is measured directly and why comparing it with the object's weight tells you, without any density calculation, whether that object will float or sink when released.

Step 1. Hang the object from a spring balance in air and note the reading. This reading is the object's true weight, WairW_{\text{air}}, since no liquid is yet pushing up on it.

Step 2. Lower the same object, still hanging from the balance, until it is fully submerged in the liquid. The reading drops to a smaller value, WapparentW_{\text{apparent}}, because the liquid is now pushing up on the object and supporting part of its weight — the spring only has to supply the rest.

Step 3. The amount by which the reading dropped is exactly the strength of the liquid's upward push. So the buoyant force is Fbuoyant=Wair−WapparentF_{\text{buoyant}} = W_{\text{air}} - W_{\text{apparent}}.

Step 4. Compare FbuoyantF_{\text{buoyant}} with WairW_{\text{air}}. If FbuoyantF_{\text{buoyant}} is less than WairW_{\text{air}}, the buoyant force can never fully support the object, and once released it sinks. If an object's shape lets the buoyant force climb to equal WairW_{\text{air}} before the object is fully submerged, the object floats at that depth instead.

Worked example

Question: A solid iron ball weighs 20 N in air. When fully lowered into a tank of water while hanging from a spring balance, the balance reads 15 N. State what happens to the ball and find the buoyant force acting on it.

Step 1. Weight in air, Wair=20W_{\text{air}} = 20 N.

Step 2. Apparent weight when fully immersed, Wapparent=15W_{\text{apparent}} = 15 N.

Step 3. Buoyant force =Wair−Wapparent=20−15=5= W_{\text{air}} - W_{\text{apparent}} = 20 - 15 = 5 N.

Step 4. Compare: the buoyant force (5 N) is far smaller than the weight (20 N), so the two forces do not balance. The ball sinks, and the buoyant force acting on it is 5 N — a compact iron ball displaces too little water to support its own weight.

Competitive stretch

If the same 20 N ball were reshaped, keeping the same weight, into a hollow bowl that displaces enough water to reach a 20 N buoyant force before going fully underwater, it would float instead — the reading on the spring balance holding it would then read 0 N, since the liquid alone would be supporting the entire weight.

Common traps

  • Thinking heavier objects always sink and lighter ones always float — the outcome depends on comparing weight with buoyant force, not on weight alone.
  • Believing a floating object has no forces acting on it — it has two, weight and buoyant force, which happen to be equal and balanced, not absent.
  • Assuming a material such as iron always sinks — the same iron sinks as a solid ball but floats when shaped hollow, because shape changes how much liquid gets displaced.
  • Reaching for a density calculation (ρ=m/V\rho = m/V) at this stage — that quantitative step belongs to a later chapter; here the reasoning stays with comparing weight and buoyant force using spring-balance readings.

Ask the tutor: Want to work through more floating-versus-sinking scenarios — coins, balloons, boats, or ice cubes — together?

If two objects are made of the exact same material, will they always both float or both sink together?

Not necessarily — shape matters just as much as material. A solid, compact chunk of a material displaces relatively little liquid for its weight, so its buoyant force stays small and it sinks. The same amount of material, spread into a hollow or wide shape, displaces far more liquid before going fully under, so the buoyant force can climb high enough to balance the weight, letting it float. This is exactly why a solid iron ball sinks while a hollow iron ship floats.

Why does the spring balance reading drop when I lower an object into water?

The spring balance only shows the force it itself must supply to hold the object up. In air, it supplies the entire weight, so the reading equals the true weight. Once the object is underwater, the liquid also pushes up on it with a buoyant force, sharing the job of holding the object up. The spring balance now only needs to supply the leftover force, so its reading drops. The size of that drop is precisely the buoyant force, which is why Fbuoyant=Wair−WapparentF_{\text{buoyant}} = W_{\text{air}} - W_{\text{apparent}}.

Does an object have to be completely underwater for a buoyant force to act on it?

No. Any part of an object that is inside the liquid experiences an upward push from that liquid, whether the object is fully submerged or only partly. A floating boat, for instance, has only its lower portion underwater, yet the buoyant force from that submerged portion alone is enough to balance the boat's entire weight. As an object sinks deeper into a liquid, more of it becomes submerged, and the buoyant force on it keeps increasing until either the object is fully underwater or the buoyant force has grown enough to equal the object's weight, at which point it floats.

Before this

Where this leads