122.1.2 - Statics & Strengths

Fundamental Statics Concepts

Equilibrium

In mechanics - both statics and dynamics - Equilibrium refers to the condition in which the net force and net torque on a body are both equal to zero. This means that the sum of all forces and moments acting on a body is zero, and the body is not accelerating or rotating.
- Static Equilibrium: A body is said to be in static equilibrium when it is at rest and the net force and net torque acting on it are both zero.
  - A classic scenario of static equilibrium is a book sitting on a table. The book is at rest and the forces acting on it are balanced, the force of gravity pulling the book down and the normal force from the table pushing the book up. The net force and net torque on the book are both equal to zero, and the book is in static equilibrium.
- Dynamic Equilibrium: A body is said to be in dynamic equilibrium when it is in motion, but the net force and net torque acting on it are both zero.
  - An example of dynamic equilibrium is a satellite orbiting around the Earth. The force of gravity pulling the satellite towards the Earth and the centrifugal force pushing the satellite away from Earth are equal, hence the satellite is in dynamic equilibrium.
In statics, equilibrium is used to determine the forces acting on a structure and ensure that the structure will remain stable and not tip over or collapse.
In dynamics, equilibrium is used to determine the forces acting on a moving body and the resulting acceleration.

Forces, Loads, Scalars, & Vectors

In engineering and physics, force and load are related but distinct concepts.
- A Force is a physical interaction that can cause a change in motion of an object. It can be defined as a push or a pull, and it is measured in units of Newtons (N) in the International System of Units (SI) or pounds (lbf) in the British system.
- A Load is a type of force that is applied to a structure or material. A load can be thought of as the weight or weight-equivalent of an object or substance that is applied to a structure or material. It is measured in units of weight such as newtons (N) or pounds (lbf).
In summary, force is a physical interaction, and load is a type of force that is applied to a structure or material.
- For example, a weight of 100kg is a load. If the weight is supported by a rope, the rope will be subject to a force of 1000N (100kg * 9.8 m/s^2) as the force is exerted by the load on the rope.
When designing structures and materials, it is important to consider both the forces and the loads that will be applied to them. Engineers must ensure that the structure or material can withstand the loads that will be applied to it without failing, and that the forces that result from the loads will not cause the structure or material to become unstable.

A Scalar is a physical quantity that has only magnitude and no direction. It is represented by a single number with a unit of measurement, and it can be added, subtracted, multiplied, and divided. Scalars are often used in conjunction with vectors to fully describe a physical situation.
- Examples of scalar quantities include:
  - Length & Distance
  - Mass
  - Volume
  - Time
  - Temperature
  - Energy
  - Electric Charge
  - Speed
A Vector is a physical quantity that has both magnitude and direction. In the context of statics and dynamics, a force or load is considered a vector because it has both a magnitude (the amount of force) and a direction (the direction in which the force is acting). This means that a force can be represented graphically as a vector arrow, with the length of the arrow indicating the magnitude of the force and the direction of the arrow indicating the direction of the force.
- For example, a force of 10 newtons acting to the right would be represented by a vector arrow pointing to the right, with a length of 10 units. A force of 20 newtons acting upwards would be represented by a vector arrow pointing upwards with a length of 20 units.
Vector representation is important because it allows us to perform vector operations, such as vector addition and subtraction, which are used to find the net force acting on a body. It also allows us to find the magnitude and direction of the net force, which is essential for understanding the behavior of a body in equilibrium.
Magnitude and direction are the minimum components that make up vectors, but they can be further defined by several components:
- Magnitude: The size or intensity of the force, measured in units of force such as newtons (N) or pounds (lbf).
- Direction: The orientation of the force, represented by a vector arrow that points in the direction of the force.
- Point of application: The location on the body where the force is applied, also known as the line of action.
- Type of force: The type of force, such as tension, compression, shear, or bending.
- Point of reference: The point where the force is measured from, it can be the point of application or a point that is defined as the reference point.
- Sense of force: The sense of the force, indicating the direction of the force with respect to a reference point.
- Reference axis: The axis around which the force is acting, it can be linear or angular.
- Intensity: The force per unit area, it can be defined for pressure, shear, and bending.
In summary, the different components that define a force/load in statics are its magnitude, direction, point of application, type of force, point of reference, sense of force, reference axis, and intensity. Understanding these components is important to be able to analyze and solve problems related to statics, such as determining the forces acting on a structure and ensuring that the structure will remain stable and not tip over or collapse.

Free Body Diagrams

Free Body Diagrams (FBDs) are a technique used in engineering and physics to represent the forces acting on a body by isolating the body and showing the forces acting on it. They are used to simplify the analysis of a problem and help to understand the forces acting on an object in a specific situation.
FBDs are important because they allow the user to clearly and easily identify the forces acting on a body, and to represent them in a way that makes it easy to apply the principles of statics and dynamics to the problem. They help to simplify the problem by breaking it down into smaller, more manageable parts, and they make it easier to understand the relationship between the forces acting on a body and the motion of the body.
FBDs can be used in a variety of situations, including:
- Analyzing the forces acting on a structure, such as a bridge or a building, to ensure that it is stable and safe.
- Analyzing the forces acting on a machine, such as a car or a robot, to understand how it moves and how to design it to be more efficient.
- Analyzing the forces acting on a biological system, such as a muscle or a bone, to understand how it works and how to design medical devices to help it function better.
When creating a FBD, you should follow these steps:
- Identify the body or system of interest and isolate it from the rest of the system.
- Draw the body and represent it as a simple geometric shape.
- Draw vector arrows to represent the forces acting on the body.
- Label each force with its magnitude, direction, and point of application.
- Indicate any known or unknown quantities, such as the mass or velocity of the body.
- Use the principles of statics and dynamics, such as equilibrium, to solve the problem.

1.2✔ CHECKPOINT

FBDs at Home/School/Work

Identify & analyze instances of equilibrium in your daily life - at home, work, and/or school:
- Identify an instance of Static Equilibrium (cannot be an example shown/used in this module)
- Identify an instance of Dynamic Equilibrium (cannot be an example shown/used in this module)
- For both examples, create Free Body Diagrams to show all the forces acting and creating the state of equilibrium
  - Recommend using either PowerPoint or Draw.io (not hand-drawn)
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.):
- The instances/scenarios in real life (picture for static + video for dynamic)
- Free Body Diagrams for both instances/scenarios
- What you did/learned

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