define and use pressure

Equilibrium of Forces

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! ⚖️

Why Does It Matter?

Equilibrium lets us predict how objects will behave. If a bridge is in equilibrium, it won’t collapse. If a boat floats, the forces of buoyancy and weight are balanced.

Pressure

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.

Pressure in Fluids

In a fluid at rest, pressure acts equally in all directions. This is why a submerged object feels a force from every side. The pressure at a depth \$h\$ is:

\$P = P_0 + \rho g h\$

where \$P_0\$ is the surface pressure (usually atmospheric). 🌊

Pressure and Equilibrium

For an object floating, the buoyant force equals the weight:

\$\rho_{\text{fluid}} V g = m g\$

Thus, \$\rho_{\text{fluid}} V = m\$. The object is in equilibrium because the upward pressure (buoyancy) balances the downward weight.

Exam Tips

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”.

Quick Practice

  1. A 10 kg crate rests on a horizontal floor. What is the normal force? 🏋️‍♂️
  2. A 2 m long beam is supported at both ends and carries a 50 N load at its centre. Find the support reactions.
  3. A scuba diver is at 10 m depth. If the water density is 1000 kg/m³, what is the pressure they feel? 💦

Key Formulae

ConceptFormula
Net Force (Equilibrium)\$\displaystyle \sum \vec{F}=0\$
Net Torque (Equilibrium)\$\displaystyle \sum \tau=0\$
Pressure\$P = \dfrac{F}{A}\$
Pressure in Fluid\$P = P_0 + \rho g h\$