How do you solve for the resultant force

Daily Dose 009 | STATICS

How do you solve for the resultant force of a force system? [PART 2]

What’s the first thing that comes to mind when you read “solve for the resultant force”?

This is a problem type that you will see, in some form, on your FE Exam.

When it comes to solving for the resultant force, don’t overcomplicate it. Instead, think of it as a puzzle piece that fits into the larger picture of engineering concepts.

Just like building blocks, these concepts build a foundational basis that you will carry forward into subjects such as Dynamics, Mechanics of Materials, and Fluid Mechanics. So, let’s roll up our sleeves and delve into it.

In this video, we get into part 2 of 2 of a FE Exam Practice Problem in the subject of STATICS, specifically revolving around how to solve for the RESULTANT FORCE OF A FORCE SYSTEM acting on a hook.

If you need review all that we did to lead up to this point, you can review it here.

Key Definition

What is a FORCE SYSTEM?

A FORCE is most commonly defined as “the cause of change in the state of motion of a particle or body”.

Formulaically, it can be defined using:

• F = ma

A FORCE is a vector quantity, having a magnitude, direction, point of application and line of action.

When MULTIPLE FORCES are acting on an object, the collection of FORCES can be referred to as a SYSTEM OF FORCES.

In this case, this FORCE SYSTEM will have a SINGLE RESULTANT FORCE manifesting itself as an action on the object.

The Process

How can you solve for the resultant force of a force system?

Many view solving for the resultant force of a larger force system as something that is difficult and time consuming.

However, there are practical, uncomplicated, steps that can be adapted to even the most complex scenarios, making these problems ones you will hope to see on your FE exam.

So with that, let’s walk through a streamlined, step-by-step approach to solving for the resultant force.

As we did previously, we’ll focus on forces operating in a two-dimensional plane, though, these principles can extend to three dimensions.

• Step 1: Read through and fully understand the Problem Statement

Carefully read through the problem statement to identify what forces are present. Sketch out a diagram denoting all the forces and their angles relative to a reference axis (typically the x-axis).

• Step 2: Break all the Forces into their individual Components

For each force, deconstruct it into its x and y components.

• F_x = F cos(θ)
• F_y = F sin(θ)
• Step 3: Bring together the Component Forces

Sum the x-component of each force to determine the collective x-component (Σ F_x).

Sum the y-component of each force to determine the collective y-component (Σ F_y).

• Σ F_x = F_1x + F_2x + …
• Σ F_y = F_1y + F_2y + …
• Step 4: Compute the Resultant Force

Compute the resultant force using the Pythagorean theorem:

• R = √((Σ F_x)² + (Σ F_y)²)
• Step 5: Determine the Direction of the Resultant Force

Calculate the angle (φ) formed between the resultant force and the reference axis (often the x-axis) using the tangent function:

• tan(φ) = Σ F_y / Σ F_x
• φ = arctan(Σ F_y / Σ F_x)
• Step 6: Interpret the Findings

Understand the significance of the resultant force’s magnitude and direction within the problem’s context. Validate the consistency and appropriateness of units.

When working through these types of problems, here are a few things to keep in mind to ensure that you are concluding the correct resultant force of the force system:

• Always verify the correct coordinate system, particularly when translating angles to components. Some instances may involve polar coordinates or other systems.
• Prior to calculations, ensure uniform units. If inconsistencies exist, convert to a unified unit system (e.g., SI units).
• Angles may originate from distinct reference lines, like horizontal or vertical. Clarify the reference line for angles.
• Account for latent forces influencing the problem, such as friction or tension.
• Pay meticulous attention to force direction. Accurate component separation hinges on this factor.
• Magnitude alone might suffice for the resultant force in some cases, while others require both magnitude and direction. Carry the problem through to ensure you are fulfilling all requisites.
• Special cases, such as parallel or perpendicular forces, can simplify complicated problems.
• Aim to grasp the real-world implications of the resultant force. This enhances problem comprehension and answer validation.
• After solving for the resultant force, considering reapplying it to equations or conceptualizing to ensure contextual coherence.

And with all of that being stated, check out the video and see how we can go about solving this type of problem in the most efficient manner.

As always, we are here to help, Prepineer

Video Review

[VIDEO] How to solve for the resultant force of a force system