Buoyancy – lab and shapes

What it shows

Archimedes' principle belongs to the topic of density and pressure. Students confirm that the upthrust equals the weight of the liquid displaced by the object, notice that the floating equilibrium position does not depend on gravity, and extend the idea of submerged volume to objects of any shape.

How to use

The Lab screen lets you set the liquid density (300–3000 kg/m³) and gravity (1–25 m/s², with quick Moon/Earth/Jupiter buttons) continuously, along with the mass and volume of a block; a beaker beside the tank shows exactly the volume of liquid displaced by the block, a direct check of the formula F_A = d·g·V_sub. The Shapes screen lets you choose a block, sphere, cone, bottle or boat of the same volume and calculates the submerged volume by numerically integrating the cross-sectional area over height — the accompanying cross-section graph shades exactly the part "integrated" up to the current depth. The Explore screen has a scale under the whole tank (it reads the mass of water plus the object while the object is still in the water) and a pressure probe you can drag to different depths to measure p = d·g·h. For a 5-litre wooden block of 800 kg/m³ in water, whether it is a block or a sphere, the submerged volume when floating is exactly 4 litres, because it depends only on the object's mass and the liquid density — switching gravity to the Moon (1.6 m/s²) does not change this submerged volume; it only makes the upthrust and the weight smaller in the same proportion.

Parameters you can change

• Screen Lab, Shapes, Explore
• Liquid density (Lab screen) 300–3000 kg/m³
• Gravity g (Lab screen) 1–25 m/s²
• Block mass (Lab screen) 0.5–20 kg
• Block volume (Lab screen) 1–10 L
• Shape (Shapes screen) Block, Sphere, Cone, Bottle, Boat
• Material (Shapes and Explore screens) Foam (150 kg/m³), Wood (800 kg/m³), Ice (920 kg/m³), PVC (1380 kg/m³), Brick (2000 kg/m³), Aluminium (2700 kg/m³), Iron (7800 kg/m³), Custom
• Custom density 100–12000 kg/m³
• Volume (Shapes screen) 1–10 L
• Show cross-section graph (Shapes screen)
• Liquid (Shapes and Explore screens) Gasoline (700 kg/m³), Cooking oil (920 kg/m³), Water (1000 kg/m³), Seawater (1030 kg/m³), Honey (1420 kg/m³), Mercury (13600 kg/m³)
• Volume (Explore screen) 1–10 L

Questions to explore

1. Why does a floating wooden block not sink deeper when you switch from Earth to the Moon?
2. A block and a sphere have the same mass and both float in the same liquid. Are their submerged volumes equal? Why?
3. When you lift a sunken iron block completely out of the water, how does the reading of the scale under the tank change?