Upthrust, Floating and Sinking Revision Notes | GCSE AQA Higher Physics

1. Why Ships Float But Stones Sink

Picture a massive cruise ship floating effortlessly on water, whilst a tiny pebble sinks straight to the bottom. This seems to defy logic - surely the heavier object should sink faster? The answer lies in understanding how fluids push back against objects placed in them.

When you submerge any object in water, the water doesn't just sit there passively. It pushes upward against the object with a force called upthrust. This upward push happens because water pressure increases with depth, creating a pressure difference between the top and bottom surfaces of the object.

The key insight is this: whether something floats or sinks depends not on its total weight, but on how much water it displaces compared to its own weight. A ship displaces enormous volumes of water, creating enough upthrust to support its weight. A stone, despite being much lighter, displaces very little water relative to its weight.

2. The Science of Upthrust

To understand upthrust, imagine lowering a cube into water. The water pressure at the bottom of the cube is greater than the pressure at the top because pressure increases with depth. This pressure difference creates a net upward force - the upthrust.

The deeper you go in any fluid, the greater the pressure becomes. This happens because the weight of all the fluid above presses down. At 10 metres underwater, you feel the weight of a 10-metre column of water pressing on every square centimetre of your body.

For a submerged object, the bottom surface experiences higher pressure than the top surface. The difference in these pressures, multiplied by the surface area, gives the upthrust force. This is why upthrust always acts vertically upward, opposing the weight of the object.

3. Archimedes' Principle - The Golden Rule

Archimedes discovered this principle over 2000 years ago, and it remains the key to understanding all floating and sinking behaviour. When you place an object in water, it pushes some water out of the way - this is called displacement. The upthrust force equals exactly the weight of this displaced water.

This principle works for any fluid, not just water. A helium balloon floats in air because it displaces air that weighs more than the balloon itself. A submarine can control its buoyancy by taking water into ballast tanks, changing how much water it displaces relative to its total weight.

The beauty of Archimedes' principle is its simplicity. You don't need to worry about the complex pressure calculations - just compare the weight of the object to the weight of fluid it displaces. If the displaced fluid weighs more, the object floats. If the displaced fluid weighs less, the object sinks.

Worked example: Calculating Upthrust Using Archimedes' Principle

A wooden block with volume 0.002 m³ is placed in water (density = 1000 kg/m³). Calculate the upthrust force. [3 marks]

1. Volume of block = 0.002 m³ Density of water = 1000 kg/m³ g = 9.8 N/kg — We need these values to find the weight of displaced water
2. Mass = density × volume Mass = 1000 × 0.002 = 2.0 kg — [1 mark] The block displaces 0.002 m³ of water
3. Weight = mass × g Weight = 2.0 × 9.8 = 19.6 N — [1 mark] This is the upthrust force by Archimedes' principle
4. Upthrust = 19.6 N — [1 mark] Always include units in your final answer

Answer: Upthrust = 19.6 N

4. The Floating and Sinking Decision

Whether an object floats or sinks comes down to a simple comparison between two forces: its weight pulling down and the upthrust pushing up. When upthrust equals weight, the object floats in equilibrium. When weight exceeds upthrust, the object sinks.

Density provides the shortcut to this decision. If an object's density is less than the fluid's density, it will float. If the object's density is greater than the fluid's density, it will sink. This is because density determines how much the object weighs compared to the same volume of fluid.

Water has a density of 1000 kg/m³. Wood typically has a density of 600-800 kg/m³, so it floats. Steel has a density of about 7800 kg/m³, so it sinks. However, a steel ship floats because its overall density (including the air-filled interior) is less than water's density.

• Object density < fluid density → object floats
• Object density = fluid density → object hovers (neutral buoyancy)
• Object density > fluid density → object sinks

5. Real-World Applications and Exam Technique

Understanding upthrust explains many everyday phenomena. Hot air balloons work because heated air is less dense than cold air, creating upthrust in the atmosphere. Fish use swim bladders to adjust their density and control their depth. Icebergs float with about 90% underwater because ice is slightly less dense than seawater.

In submarine design, ballast tanks allow precise control of buoyancy. To dive, the submarine takes water into its ballast tanks, increasing its overall density. To surface, compressed air blows the water out, decreasing density and creating positive buoyancy.

Ships demonstrate the importance of shape in buoyancy. A solid steel block sinks, but the same steel formed into a hollow ship displaces enough water to create sufficient upthrust. The key is maximising the volume of water displaced whilst minimising the object's weight.