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Rigid Body Statics

Fundamentals: Are you ready to explore the world of rigid bodies?

In this chapter, we will dive into the fascinating world of rigid body mechanics and explore:

  • The invisible forces that act on objects and set them in motion or slow them down.
  • The secret of cutting free, which allows us to isolate the most important forces acting on an object.
  • The magical free body diagrams, which show us how forces and moments act on an object.
  • The rigid body and its six degrees of freedom, which give it its mobility.
  • The 6 axioms of rigid body statics, which are the foundation for everything we know about objects at rest.

Are you ready to uncover these secrets?

Then buckle up and let's go on an exciting journey into the world of rigid body mechanics!

It's going to be exciting!

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Table of Contents

4.1 The Equilibrium Axiom

The Physics of Tug-of-War: How the Equilibrium Axiom of Rigid Body Mechanics Works

Imagine two cute little puppies, Einstein and Newton, discovering a rope in the garden. Both are super excited and want to play with the rope. Einstein grabs one end with his sharp teeth, while Newton holds on tight to the other end. What happens now?

Einstein pulls to the right with all his might, Newton resists with his little paws and pulls to the left. The two puppies bark and growl with exertion, but the rope doesn't move an inch. Why is that? The equilibrium axiom tells us why.

puppy, tug of war
Forces in Equilibrium

Forces are everywhere. They can move us, hold us down, or throw us into the air. In equilibrium, two or more forces are present when they cancel each other out.

Einstein and Newton pull on the rope with their teeth and paws. These tensile forces act in opposite directions. Since the puppies are equally strong, the two forces cancel each other out. That's why the rope doesn't move.

In rigid body mechanics, we consider the rope as a rigid body. This means we simplify the rope so that it doesn't stretch or elongate when Einstein and Newton pull on it. With this idealization, we can apply our example to all rigid bodies.

Conditions for Equilibrium

For two forces to be in equilibrium, they must meet the following conditions:

  • They must be equal in magnitude.
  • They must be oppositely directed.
  • They must have the same line of action.

The line of action is the imaginary line along which the force acts.

This figure 2.4.1 shows a box being loaded by two equally large forces and is in equilibrium.
Fig. 2.4.1: Box in equilibrium

The graphic shows a box standing on a horizontal plane. Two equal forces F act on the box. The forces are oppositely directed and lie on the same line of action. The box is in equilibrium because the sum of the two forces is zero.

Examples from Practice
  • Bridge construction: Bridges must be designed so that the weight of the bridge is balanced by the force of the piers.
  • Building construction: Buildings must be built to withstand wind loads and other external influences.
  • Mechanical engineering: Machines must be designed so that the forces acting on them are in equilibrium so that they function smoothly.
Conclusion

The equilibrium axiom is an important principle of physics that finds application in many areas of everyday life. By understanding how equilibrium forces work, we can build stable and functional structures and design machines.

Additional Information
  • Vector addition: Vector addition is the addition of two or more vectors. Vectors are quantities that have both a magnitude and a direction, like our forces in Fig. 2.4.1.
  • Resultant: The resultant is the sum of all forces acting on a body. It is zero for an object in equilibrium.
  • Equilibrium group: A group of forces in which there is no resultant is also called an equilibrium group.