8.1 Static Equilibrium and Torque

Static Equilibrium Overview

• Static Equilibrium Definition: Condition where an object remains at rest, with no net force or net torque acting on it.

• Key Conditions for Static Equilibrium of an Extended Object:

  • $\sum \vec{F} = 0$ (Net force must be zero)

  • $\sum \tau = 0$ (Net torque must be zero)

Importance of Torque in Static Equilibrium

• Objects can be at rest but not in equilibrium if net torque is not zero.

• For extended objects (e.g., beams, ladders), both net force and net torque conditions must be satisfied.

Example Problem: Lifting a Load

1. Scenarios: Analyze a static equilibrium problem with forces acting on a beam.

2. Force Summation:

   • $\sum F<em>y = F</em>m + F<em>p - F</em>b = 0$

3. Torque Calculation:

   • Apply torque conditions at a pivot point.

   • $\sum \tau = F<em>b \cdot d</em>b - F<em>m \cdot d</em>m = 0$

4. Outcomes: Calculate man’s force and pivot force.

Choosing a Pivot Point

• Selecting pivot where an unknown force acts simplifies calculations (no torque contribution from this force).

• Example: If analyzing a hammer supported at different pivots, net torque will still be zero at any point due to static equilibrium.

Problem-Solving Approach for Static Equilibrium

• Strategize: Identify object of interest and choose a pivot point.

• Prepare: Draw a clear diagram showing all forces and distances related to the pivot.

• Solve: Use conditions $\sum \vec{F} = 0$ and $\sum \tau = 0$ to set up equations and solve.

• Assess: Check results for reasonableness.