122.1.4 - Statics & Strengths

Calculating Forces

Force Systems

A Force System may be defined as any number of forces that are
collectively considered.
- There are three broad classifications of force
  systems:
  - A Collinear Force System is one in which the lines of action of all the forces lie on the same line. They can be considered to be 1-Dimensional (1D).
  - A Coplanar Force System is one in which the lines of action of all the forces lie in the same plane. They can be considered to be 2-Dimensional (2D).
  - A Noncoplanar Force System is one in which the lines of action of all the forces do not lie in the same plane. They can be considered to be 3-Dimensional (3D).
- The coplanar and noncoplanar force systems may be further classified:
  - Concurrent Force Systems occur when the lines of action of all the forces intersect at a common point
  - Non-concurrent Force Systems occur if the action
    lines do not intersect at a common point and are not parallel.
  - Parallel Force Systems occur if the lines of action of all the forces
    are parallel
- The different classifications of force systems may therefore be summarized as follows:
  - Collinear
  - Coplanar concurrent
  - Coplanar non-concurrent
  - Coplanar parallel
  - Noncoplanar concurrent
  - Noncoplanar non-concurrent
  - Noncoplanar parallel

Force Calculation Methods

When multiple forces are applied on an object, the net sum of the forces is called the Resultant, which can be calculated from the magnitude and direction of the force vectors
- The magnitude of the resultant force is the square root of the sum of the squares of the individual forces
- The direction of the resultant force is the direction in which the forces are acting.
- The object is in equilibrium if the resultant force is zero, meaning that the object is either at rest or moving at a constant velocity.
- If the resultant force is not zero, the object is in motion and experiencing an acceleration.
There are several methods for calculating resultant forces, which can be divided into two categories:
- Graphical Methods:
  - Head-to-Tail Method: This method involves aligning the tail of each vector with the tip of the preceding vector and then drawing the vector from the tail of the first vector to the tip of the last vector. The vector thus obtained is the resultant force.
  - Parallelogram Method: This method involves drawing a parallelogram with the vectors as adjacent sides. The diagonal of the parallelogram that connects the opposite corners is the resultant force.
- Analytical Method: The analytical method for calculating the resultant force of a force system involves using vector algebra. The steps for performing the analytical method are:
  - Write the vector equation for each force in the system: Each force in the system is represented by a vector, with the magnitude and direction of the force. The vector equation for each force should be written in terms of its magnitude and direction.
  - Sum the vector equations to get the vector equation of the resultant force: The vector equations for each force in the system can be added together using vector algebra. The sum of the vectors is the vector equation of the resultant force.
  - Use the magnitude and direction of the resultant force vector to determine the magnitude and direction of the force: The magnitude of the resultant force vector is the square root of the sum of the squares of the individual forces. The direction of the resultant force vector is the direction in which the forces are acting.

Force Units & Formulas

1.4✔ CHECKPOINT

Calculate Forces at Home/Work/School

Continue analyzing the examples you used in the previous checkpoints for static and dynamic equilibrium:
- Calculate the magnitudes and directions of all the forces involved
  - Show your work for all your calculations
- Calculate the sum of all your forces for each example
Once done, add documentation to your previously-created "Intro to Statics" Project page on your portfolio website, showing/describing (via: text, pictures, gifs, videos, etc.):
- Your force calculations & how you calculated them
- The sum of all your forces, & how you calculated them
- What you did/learned

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