define and use pressure

What is Equilibrium?

When all forces acting on an object cancel each other out, the object is in static equilibrium. In this state:

• Net force is zero: $\displaystyle \sum \vec{F}=0$
• Net torque is zero: $\displaystyle \sum \tau=0$

Think of a perfectly balanced seesaw. If the weights on both sides are equal, the seesaw stays level – that’s equilibrium! ⚖️

Definition

Pressure is the force applied per unit area:

$$P = \frac{F}{A}$$

Units: Pascal (Pa) = $\displaystyle \frac{\text{N}}{\text{m}^2}$.

Imagine pressing your palm on a table. The harder you press (larger $F$) or the smaller the area of your palm (smaller $A$), the higher the pressure. 💪🖐️

Common Examples

• Water pressure increases with depth: $P = \rho g h$.
• Air pressure at sea level: ~101 kPa.
• Pressure in a tyre: ~200 kPa.

Tip 1: Always check both force and torque when solving equilibrium problems.

Tip 2: Remember $P = \frac{F}{A}$ – if you’re given force and area, you can find pressure directly.

Tip 3: For fluids, use $P = P_0 + \rho g h$. Identify which depth $h$ is relevant.

Tip 4: When a problem mentions “balanced”, think “net force = 0” and “net torque = 0”.