Buoyant force

The push from all sides. When an object is lowered into a liquid — fully or partly — the liquid presses on it from every direction: from below, from above, and from the sides. The sideways pushes cancel each other out because the liquid pressure at the same depth is the same all around. What survives is a net upward push, because liquid pressure increases with depth, so the push from below (at greater depth) is stronger than the push from above (at shallower depth). That surviving net upward push is the buoyant force.

Measuring it with a spring balance. The same spring balance used elsewhere in this chapter to measure weight can measure the buoyant force too. Hang the object from the balance and read its weight in air. Then, without removing it from the hook, lower the object into a beaker of water so it is fully immersed. The reading drops. This "loss of weight" is exactly the buoyant force the liquid is exerting:

where: weight in air is the spring-balance reading with the object hanging in open air, apparent weight in liquid is the reading once the object is fully immersed, and both are read straight off the balance in newton (N). This is plain subtraction of two spring-balance readings — never a density calculation — matching the whole-number N values used throughout the "Exploring Forces" chapter.

Deciding float or sink. Once you know the buoyant force and the weight, one comparison settles the object's fate:

• weight greater than buoyant force → the object sinks
• weight equal to buoyant force → the object floats

Archimedes' Principle, in words. The rule connecting all of this is Archimedes' Principle, used here only qualitatively: an object that is fully or partially immersed in a liquid experiences an upward buoyant force equal to the weight of the liquid it displaces. Pushing an object into a liquid shoves aside ("displaces") some liquid to make room, and it is the weight of exactly that displaced liquid which pushes back on the object. No formula involving volume or density is needed at this stage — that connection is built later, once density itself has been introduced.

This topic is purely qualitative at Class 8 level, so instead of a formula-derivation, here is the reasoning that explains why a liquid pushes upward at all — the physical picture behind the spring-balance rule above, using nothing but pressure-with-depth reasoning that is well within syllabus scope. Picture a cube-shaped block immersed in water. Water pressure exists on every face of the cube, and pressure always pushes perpendicular into a surface. On the four side faces, the pushes are horizontal and, at any given depth, equal and opposite from left-right and front-back — they cancel completely, so the block feels no net sideways force. That leaves only the top and bottom faces. The top face sits at a shallower depth than the bottom face, and liquid pressure is known to increase with depth — a swimmer feels the water press harder on their ears the deeper they dive. So the water pushes down on the top face less strongly than it pushes up on the bottom face. Subtracting the weaker downward push from the stronger upward push leaves a net force pointing straight up. That net upward force, arising purely because pressure grows with depth, is the buoyant force. It exists on every submerged object regardless of shape, which is why even oddly shaped stones and metal balls feel this same upward push, and why the spring-balance method above — simply reading the "loss of weight" — is a reliable stand-in for reasoning through all these pressure differences face by face.

Question. A metal ball is hung from a spring balance. In air, the balance reads 12 N. When the same ball is fully lowered into a beaker of water while still hanging from the balance, the reading changes to 9 N. Find the buoyant force exerted by the water on the ball, and state whether the ball floats or sinks.

Step 1. Read off the two spring-balance values directly from the question: weight in air = 12 N, apparent weight fully immersed in water = 9 N.

Step 2. Apply the loss-of-weight rule: buoyant force = weight in air minus apparent weight in liquid = 12 N − 9 N = 3 N.

Step 3. Compare the buoyant force with the ball's actual weight to decide its fate: the weight (12 N) is far greater than the buoyant force (3 N), so the upward push is nowhere near enough to support the ball.

Step 4. Conclude: since weight is greater than buoyant force, the ball sinks to the bottom of the beaker. Final answer: buoyant force = 3 N; the ball sinks.

Competitive stretch

A block of wood weighs 5 N in air. If the same block were held fully submerged, the water would push up on it with a buoyant force of 8 N. What happens when the block is simply released in a tub of water?

Step 1. While fully immersed, compare the two forces: buoyant force (8 N) is greater than weight (5 N), so the net effect is upward — the block accelerates toward the surface rather than staying down.

Step 2. As the block rises, less of it stays underwater, so it displaces less liquid and the buoyant force on it shrinks from its fully-submerged value of 8 N.

Step 3. The block keeps rising only until the shrinking buoyant force falls to exactly match its unchanging weight of 5 N. At that point the two forces balance and the block stops rising further. Final answer: the block floats, partly above and partly below the surface, once buoyant force equals weight (5 N).

• Thinking buoyant force only acts on floating objects — every object in a liquid feels an upward buoyant force, even a stone that sinks straight to the bottom.
• Mixing up "weight in air" with "apparent weight in liquid" — the drop in the spring-balance reading is the buoyant force, not a change in the object's true weight.
• Assuming floating or sinking depends on size or material alone rather than on comparing weight with buoyant force — a huge steel ship floats while a tiny steel pin sinks, because it is this force balance, not the material by itself, that decides.
• Bringing in density or $\rho = m/V$ to explain buoyancy at this stage — density belongs to a later chapter; here, buoyancy is explained purely by comparing weight and buoyant force via spring-balance readings.

Ask the tutor: Curious why a heavy iron ship floats while a small iron nail sinks — ask the tutor to work through the force comparison with you.