5.1 Equilibrium

Newton's Laws Overview

• Forces govern the motion of objects.

• Equilibrium: Net force is zero (static or dynamic).

• Dynamics: Relate forces to motion; accelerations depend on net forces.

Equilibrium Concepts

• Static Equilibrium: Object at rest; all forces balanced.

• Dynamic Equilibrium: Constant velocity; net force still zero.

• Free Body Diagrams (FBD): Visual representation of forces acting on an object.

Static Equilibrium Example

• Example: Octopus hanging motionless; net force = 0, forces balance.

• Forces acting: Weight (down) & tension (up); equal magnitude.

Dynamic Equilibrium Example

• Example: Hover puck slides on air cushion at constant speed.

• Constant speed implies net force = 0.

Newton's Second Law

• Acceleration related to net force: $F_{net} = m imes a$.

• In equilibrium: $F_{net} = 0$.

Force Summation

• Net force determined as the vector sum of all forces acting on an object.

• In two dimensions:

• $F<em>{net, x} = F</em>{1x} + F_{2x} + …$

• $F<em>{net, y} = F</em>{1y} + F_{2y} + …$

• Equilibrium equations:

• $ext{Sum of } F_x = 0$

• $ext{Sum of } F_y = 0$

Problem Solving Strategy

• Check for equilibrium: Is acceleration zero?

• Identify forces; create FBD.

• Set up equilibrium equations.

• Solve for unknown forces.

Example Problems:

• Finding tension in ropes:

• Static equilibrium requires net force to be zero.

• Apply FBD and equations to find tension.

• E.g., tension in a hanging orangutan = weight.

Dynamic Equilibrium Example

• Example: Towing a car; analyzing forces through tension in tow rope.

• Requires understanding of vertical and horizontal components of tension.