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The mechanical engineering principles describe the foundations for the operation of mechanical systems. These principles deal mainly with concepts like force, energy, and motion by defining them through mathematical problems and equations.

It is important to highlight that mechanical engineers need a broad set of skills, which should be based on basic principles. Here’s a great view on the main skills required and how they are required to be successful, based on a study conducted by the Bureau of Labor Statistics of the United States in 2015.

Clearly, the skills to deal with the mathematical problems and equations that define the mechanical engineering principles are the most important.

Although it is a broad and diverse science, the basic principles of mechanical engineering can be summarized with the table below: Principle What it involves What areas are covered (not limited to) Mechanics Studying forces and their effects. Statics, dynamics, fluid mechanics, kinematics, and strength of materials. Thermodynamics Studying energy, how it is transformed and how it can be used through a system. Heat transfer, state changes, and the application of heat power in complex systems. Mechanical Design Designing mechanisms and their components for optimal performance. Procedures to move a concept from idea to reality, including sketches, technical drawings, 3D models, compliance with norms and standards, among other aspects. Structures and Machines Analyzing the performance of structural designs, mechanisms, and assemblies as a whole by means of specific testing and software simulations Prototyping, Finite Element Analysis (FEA), Computational Fluid Dynamics (CFD), among others.

In this article, we provide an overview of the basic concepts of mechanics, the first of these principles. The concepts covered include:

• Force
• Torque
• Work
• Power

### What is force?

Force is one of the most basic concepts in mechanical engineering principles, which makes the basis for the definition of other important aspects.

Simply put, a force is anything that has an effect on a body that tends to alter the state of motion of that body. Mathematically speaking, a force is a vector. This means it has a magnitude and a direction, and both must be used to fully describe it.

A force is usually described as one of two effects:

• Push effect
• Pull effect

Any of these two effects results from the interaction between two or more bodies. Whenever there is an interaction, there is, at least, one force affecting each of the bodies. The force will no longer affect the bordes only when the interaction stops.

Forces are considered to be the causes of linear motion, and this effect is defined by Newton’s Laws. This is the reason to use Newton as the standard metric unit for force.

One Newton is the amount of force required to give a 1 kg mass an acceleration of 1 m/s2. And the equation to calculate the force is:

Force = mass x acceleration

F = m x a = 1 kg x 1 m / s2

### What is torque? Torque is a special type of force because instead of causing linear motion, it causes rotational motion, which is why it is also called rotational force.

A common example of torque is when an axle is rotated by pushing on a rod or lever. Likewise, a linear force at a distance from the center of the axle can be generated by applying torque on the axle.

Torque equals force multiplied by moment arm and it is mathematically represented by the following relationships:

T = FR or F = T/R

Where:

T is the torque in newton-meters

F is the force (Newtons)

R is the radius or distance from the center to the edge (meters)

R is also sometimes called the moment arm. The force, F, is applied perpendicular to the radius, lever or moment arm.

### What is work?

The concept of work is usually referred to as an activity involving a force and motion in the same direction of the force. Therefore, it exists when the vector of the force points in the direction of the movement or, at least, there are components of the vector pointing in that direction.

The relation described can be represented by:

Work = Force x distance moved in direction of force; where work is measured in Joules (J), the force in Newtons, and the distance in meters

J = N x m

Mathematically, work can be expressed by the following equation:

W = F x d x cos Θ where F is the force, d is the displacement, and the angle (theta) is defined as the angle between the force and the displacement vector.

### What is power?

Power is defined as the rate at which work is done. In other words, it is a function of work and time. It can be mathematically represented by using the following equation.

Power = work / time = (force x displacement) / time

The standard metric unit of power is the Watt. From the equation above, it can be deduced that a Watt is equivalent to a Joule/second.

A common term for power is horsepower, which is generally used to describe the power delivered by a machine, such as the engine of a car. One horsepower is equivalent to approximately 750 Watts.

Most machines are designed and built to do work on objects. All machines are typically described by a power rating. The power rating indicates the rate at which that machine can do work upon other objects. Thus, the power of a machine is the work/time ratio for that particular machine. The power rating relates to how rapidly the engine can accelerate the car.