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At the end of this section you should be able to:
Define “particle” and “equilibrium”
Properly draw FBD for 2D and 3D particle
Correctly identify forces acting on a particle
Properly calculate a unit vector in 2D and 3D
Create scalar equilibrium equations from FBD
Use Mathematica to perform solve steps
Understand how to model linear springs and their associated equations
Master particle equilibrium in 2D and 3D by learning the standard statics problem-solving workflow. You will define particle and equilibrium, draw accurate free body diagrams, identify forces such as tension and spring forces, compute unit vectors, write scalar equilibrium equations from the FBD, and use Mathematica for solving, with worked examples that include cable systems, bars, and spring-supported particles.
2D Particle Equilibrium
2D Particle Equilibrium
Hibbeler 13e 3.35: Solving for the maximum allowed weight causing tension in two ropes
Hibbeler 13e 3.35: Solving for the maximum allowed weight causing tension in two ropes
Plesha 2e 3.2: Solving for tension in two ropes
Plesha 2e 3.2: Solving for tension in two ropes
Plesha 2e 3.4: Solving for tension in rope and force in a bar
Plesha 2e 3.4: Solving for tension in rope and force in a bar
Springs
Springs
Plesha 2e 3.69: Solving 2D particle equilibrium with spring. This problem also features an inclined plane and normal force
Plesha 2e 3.69: Solving 2D particle equilibrium with spring. This problem also features an inclined plane and normal force
Hibbeler 13e 3.28: Solving for tension in multiple ropes with multiple FBDs
Hibbeler 13e 3.28: Solving for tension in multiple ropes with multiple FBDs
Hibbeler 13e 3.15: Solving 2D particle equilibrium with spring
Hibbeler 13e 3.15: Solving 2D particle equilibrium with spring
3D Particle Equilibrium
3D Particle Equilibrium
Hibbeler 13e F3.11: Solving for tension in three ropes supporting a load in equilibrium
Hibbeler 13e F3.11: Solving for tension in three ropes supporting a load in equilibrium
Hibbeler 13e 3.49: Solving for the maximum allowable load before a rope fails in tension
Hibbeler 13e 3.49: Solving for the maximum allowable load before a rope fails in tension
Plesha 2e 3.87: 3D particle equilibrium problem using unit vectors. This problem is solvable by hand
Plesha 2e 3.87: 3D particle equilibrium problem using unit vectors. This problem is solvable by hand
Plesha 2e 3.90: 3D particle equilibrium problem using unit vectors. This problem could be solved by hand, we use Wolfram Alpha to calculate final numeric values
Plesha 2e 3.90: 3D particle equilibrium problem using unit vectors. This problem could be solved by hand, we use Wolfram Alpha to calculate final numeric values
Hibbeler 12e 3.59: 3D particle equilibrium problem using unit vectors. We use Wolfram Alpha to perform algebra for the problem.
Hibbeler 12e 3.59: 3D particle equilibrium problem using unit vectors. We use Wolfram Alpha to perform algebra for the problem.
Mathematica Code
Mathematica Code
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