310105b Equilibrium and Mechanical Advantage 2025 TF

MOTION AND FORCE

• Description of key concepts regarding force, equilibrium, and mechanical advantage.

Objectives

• Objective 4 310105b

EQUILIBRIUM TORQUE

• Equilibrium Condition: Correct torque condition is when net torque (Στ) equals 0.

Torque Fundamentals

• Symbol: τ

• Formula: τ = F • r

• Units: Newton-meters (Nm)

NET TORQUE CALCULATIONS

• Net Torque (τnet): τnet = Στ

• Example Calculations:

  • For a force of 7N applied perpendicular to a moment arm of 14 m:

    • τ = 7N • 14m = 98Nm

  • For a force of 3N applied perpendicular to a torque moment of 1.24m:

    • τ = 3N • 1.24m = 3.72Nm

  • For 5.7Nm from a 5m arm, rearranging gives:

    • τ = F • r = 5.7Nm

• An object is in equilibrium when all forces counteract acceleration, and the object remains stationary.

EXAMPLES OF TORQUE

• Given a counter-clockwise (CCW) 8N force at 3m and a clockwise (CW) 10N force at 2m:

  • τCCW = 8N • 3m = 24Nm

  • τCW = -10N • 2m = -20Nm

  • Net Torque: τnet = τCCW + τCW = 24Nm + (-20Nm) = 4Nm

EQUILIBRIUM FORCE

• Condition for Equilibrium: ΣF = 0 (the moment is not rotating)

• Example given:

  1. CCW force: 20N at 13m → τCCW = 20N • 13m = 260Nm

  2. Find Force for FCW at 12m:

  • τCW = -F • 12m

  • Setting equal gives:

  • 260Nm = τCW = -F • 12m, compute FCW = 21.7N

SIMPLE MACHINES

• Simple Machines: Basic mechanical devices that multiply force to do work.

• Work Equation: W = Fa • d

• Allows trade of force for distance.

Mechanical Advantage

• Mechanical advantage (MA) reflects force advantage:

  • MA = Load / Effort

  • Where:

    • Load = Output force

    • Effort = Input force

    • Load distance = height the load moves

    • Effort distance = distance the effort moves

TYPES OF SIMPLE MACHINES

• Lever: Input force moves load around a pivot (fulcrum).

• Wheel & Axle: Input force applied to axle moves the wheel.

• Pulley: Using a rope to lift loads, allows for efficient force application.

• Definitions:

  • Torque = Moment

  • Perpendicular force applied influences moment/torque.

WORK EXAMPLES

• To lift a 4kg block vertically:

  • Calculate Force: F = m • g = 4kg • 9.81m/s² = 39.24N

  • Work done to lift = W = 39.24N • 5m = 196.2J

  • Work on inclined plane vs straight lift = same amount of work.

WHEEL AND AXLE MECHANICS

• Trade-off: Sacrificing force for distance to achieve work.

• Mechanical Advantage (MA): MA = Effort Distance / Load Distance.

PULLEYS AND BLOCK AND TACKLE

• Effort applies to rope to lift loads.

• Distance involved is the amount of rope pulled.

• Weight of the load being lifted matters for effort calculation.

GEAR MECHANICS

• Gears convert rotational motion to torque, affecting mechanical advantage through gear ratio.

• Example:

  • Diameter-based examples help define relationships between driver and driven pulleys in systems.

HYDRAULIC MECHANICS

• Discusses relationships and calculations involving forces in hydraulic systems, showing how force can be amplified via area ratios.