Upthrust

Overview

Upthrust is not a new type of force rule to memorise separately. It comes from the pressure at the bottom of an object being greater than the pressure at the top when the object is in a fluid.

What You Need to Know

• A fluid exerts pressure on every surface of an object in contact with it.
• Pressure is greater at greater depth, so the upward force on the bottom surface can be larger than the downward force on the top surface.
• Upthrust equals the weight of the fluid displaced by the object.
• For a fully submerged object, upthrust = rho g V, where rho is the fluid density and V is the submerged volume.
• Floating requires vertical force equilibrium: upthrust equals weight.

How to Work Through It

1. Start by drawing the pressure forces on the top and bottom of a submerged block.
2. Link the pressure difference to the resultant upward force.
3. Use Archimedes’ principle to calculate upthrust for objects in different fluids.
4. Compare weight and upthrust to decide whether an object sinks, floats, or accelerates upward.

Check Your Understanding

• Why is the upward pressure force usually larger than the downward pressure force?
• What volume should be used in upthrust = rho g V?
• How can an object float even if it is made from a material denser than water?
• What happens if weight is greater than upthrust?

Common Mistakes

• Using the density of the object instead of the density of the fluid in the upthrust equation.
• Using the total object volume when only part of it is submerged.
• Saying that floating objects have no weight.

Next Steps

• Practise drawing vertical force diagrams for floating and sinking objects.
• Revisit pressure differences if the origin of upthrust is still unclear.