Hooke's law and liquid pressure

What it shows

Two classic experiments share one screen. On the left, a spring obeys Hooke's law, F = kΔl: the extension is proportional to the load up to the elastic limit, beyond which the spring deforms plastically and the force–extension graph is no longer a straight line. At equilibrium the spring force balances the weight, so Δl = mg/k. On the right, the pressure in a liquid at rest increases linearly with depth, p = p₀ + ρgh, and depends only on depth and density, not on the shape of the container, which is why connected vessels fill to the same level.

How to use

Start with the spring: change Hanging mass and Spring constant k and compare the equilibrium extension with mg/k, then drag the mass down and release it to see it oscillate about equilibrium. Keep adding mass until the elastic limit is passed and watch the graph. Next, drag the measuring point in the vessel or set Measuring point depth h, and vary Liquid density ρ from 700 kg/m³ up to mercury while reading ρgh.

Parameters you can change

• Spring constant k 20–200 N/m
• Hanging mass 0.1–2 kg
• Measuring point depth h 0–10 m
• Liquid density ρ 700–13600 kg/m³

Questions to explore

1. If you double the hanging mass, what happens to the extension, and does this still hold beyond the elastic limit?
2. At the same depth, how many times greater is the pressure due to mercury than the pressure due to water?
3. Using the liquid pressure model, why is the base of a dam built thicker than its top?