Properties of Solids and Liquids Cheatsheet

Cheat Codes & Shortcuts

• Density: \( \rho = \frac{m}{V} \), mass per unit volume.
• Pressure in Liquids: \( P = \rho g h \), pressure at depth \( h \).
• Buoyancy: Buoyant force \( F_b = \rho_f V g \), where \( \rho_f \) is fluid density.
• Young’s Modulus: \( Y = \frac{\text{stress}}{\text{strain}} = \frac{F/A}{\Delta L / L} \).
• Bulk Modulus: \( K = -\frac{\Delta P}{\Delta V / V} \), measures incompressibility.
• Pascal’s Principle: Pressure applied to a confined fluid is transmitted equally.
• Viscosity: Resistance to flow, \( F = \eta A \frac{dv}{dy} \), where \( \eta \) is viscosity.
• Surface Tension: \( T = \frac{F}{L} \), force per unit length on liquid surface.
• Hooke’s Law: \( F = -k \Delta x \), for elastic solids under small deformations.
• Continuity Equation: \( A_1 v_1 = A_2 v_2 \), for incompressible fluids.

Quick Reference Table

Advice

Properties of Solids and Liquids Quick Tips

• Density: Use \( \rho = \frac{m}{V} \) to compare materials; denser objects sink in less dense fluids.
• Hydrostatic Pressure: Apply \( P = \rho g h \) for liquids at rest; depth is key.
• Buoyancy: Use Archimedes’ principle, \( F_b = \rho_f V g \), for objects in fluids.
• Elasticity: For solids, use \( Y = \frac{\text{stress}}{\text{strain}} \) to measure stiffness.
• Fluid Flow: Apply continuity equation \( A_1 v_1 = A_2 v_2 \) for steady, incompressible flow.