When all forces acting on an object cancel each other out, the object is in static equilibrium. In this state:
Think of a perfectly balanced seesaw. If the weights on both sides are equal, the seesaw stays level – that’s equilibrium! ⚖️
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 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. 💪🖐️
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). 🌊
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.
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”.
| Concept | Formula |
|---|---|
| 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\$ |