Essential Engineering Mechanics Principles and Formulas

1. What is a Free Body Diagram (FBD)?

A Free Body Diagram (FBD) is a simple sketch that shows all the forces acting on an object. The object is usually represented as a dot or a simple shape, and arrows are used to show the direction and magnitude of each force. The purpose is to help analyze how forces affect the object's motion.

2. What is a Co-planar Concurrent Force System?

A co-planar concurrent force system is a set of forces that all lie in the same plane and meet at a single point. In this system, the forces act on the same object but are applied from different directions.

• Co-planar: Forces exist on the same flat surface.
• Concurrent: All force vectors intersect at one common point.

3. Equilibrium Equations for a Body in Space

The equilibrium equations for a body in 3D space are:

• ∑F_x = 0 (Sum of all forces in the x-direction)
• ∑F_y = 0 (Sum of all forces in the y-direction)
• ∑F_z = 0 (Sum of all forces in the z-direction)
• ∑M = 0 (Sum of all moments/torques about any point)

These equations ensure that the body is not moving or rotating, indicating a state of static equilibrium.

4. Parallel Axis Theorem for Moment of Inertia

The Parallel Axis Theorem states that the moment of inertia (I) of an object about any axis parallel to the axis through its center of mass is calculated as:

I = I_cm + Mh²

• I: Moment of inertia about the new axis.
• I_cm: Moment of inertia about the center of mass axis.
• M: Mass of the object.
• h: Distance between the center of mass and the new axis.

5. Relation Between Joints and Members in a Perfect Truss

In a perfect truss, the relationship between the number of joints (j) and the number of members (m) is defined by the equation:

m = 2j - 3

• m: Number of members.
• j: Number of joints.

This relation ensures that the truss is stable and statically determinate.

6. What is Wedge Friction?

Wedge friction refers to the frictional force that resists the motion of an object when it is pushed or pulled along a wedge-shaped surface. It occurs when a force is applied to an object on a wedge, causing it to move along the inclined surface. The frictional force depends on the wedge angle, the normal force, and the coefficient of friction between the contact surfaces. Essentially, wedge friction prevents an object from sliding easily on the sloped surface.