Contents

###### Daily Dose 008 | STATICS

#### How do you find the resultant force of a set of forces acting on a hook? [PART 1]

How do you find the resultant force?

This will most definitely be a statement you read, in some form, on the day of your FE Exam.

Without a doubt, aside from the pure Mathematics, the most broadly applied subject you will encounter in the practice of engineering is Statics.

The theories found within this subject are foundational to much of the material you will encounter in the areas of Dynamics, Mechanics of Materials, Fluid Mechanics amongst others – so with that, we need to get to work.

In this video, we dive in to a FE Exam Practice Problem in the subject of STATICS, specifically revolving around determining the RESULTANT OF A FORCE SYSTEM acting on a hook…this is PART 1 of 2 for this particular problem.

###### 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 find the resultant force of a force system?

Finding the resultant force in a force system can certainly present itself as difficult, but in practice, it involves some simple, straightforward steps that can be applied across the most complicated scenarios.

Let’s run through a simplified step by step process to getting these problems done quickly and efficiently on the FE Exam.

We will assume we are dealing with forces acting in a two-dimensional plane, but the principles can be extended to three dimensions, but let’s keep it simple for now.

**Step 1: Understand the Problem****Step 2: Break Forces into Components**- F
_{x}= F cos(θ) - F
_{y}= F sin(θ) **Step 3: Sum up the Components**- Σ F
_{x}= F_{1x}+ F_{2x}+ … - Σ F
_{y}= F_{1y}+ F_{2y}+ … **Step 4: Calculate the Resultant Force**- R = √((Σ F
_{x})^{2}+ (Σ F_{y})^{2}) **Step 5: Find the Direction of the Resultant Force**- tan(φ) = Σ F
_{y}/ Σ F_{x} - φ = arctan(Σ F
_{y}/ Σ F_{x}) **Step 5: Interpret the Results**

Read the problem statement carefully and identify the forces involved. Sketch a diagram labeling the forces and the angles they make with a reference axis (often the x-axis).

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

Add up all the x-components of the forces to find the total x-component (Σ F_{x}).

Add up all the y-components of the forces to find the total y-component (Σ F_{y}).

The resultant force can be found using the Pythagorean theorem:

Calculate the angle (φ) that the resultant force makes with the reference axis (often the x-axis). You can use the tangent function for this:

Understand what the magnitude and direction of the resultant force imply in the context of the problem. Make sure the units are consistent and make sense.

Here are some additional tips to consider when being asked to find the resultant force of a force system:

- Always confirm you are using the correct coordinate system, especially when converting angles to components. In some cases, the problem might use polar coordinates or another system.
- Make sure that all units are consistent before doing any calculations. If they are not, convert them to a common unit system (SI units, for example).
- Angles can sometimes be given from different reference lines, such as from the horizontal or from the vertical. Always clarify which reference line is being used for the angles.
- Keep an eye out for additional forces that may not be directly mentioned in the problem but can have an effect, like friction or tension.
- Pay close attention to the direction in which each force is acting. This is crucial for splitting the force into its components correctly.
- Sometimes the problem may be asking only for the magnitude of the resultant force, but other times it may also require the direction. Ensure you are providing all the information requested.
- Be aware of special cases, such as when all forces are parallel or perpendicular to each other, as these can often simplify the problem.
- Try to understand what the resultant force means in the context of the real-world situation being described. This will not only help you understand the problem better but will also provide a sanity check for your answer.
- After you’ve found the resultant force, it’s often a good idea to plug it back into the equations or to think about it conceptually to make sure the answer makes sense in the context of the problem.

By following these steps, and keeping these tips in mind, you will quickly and efficiently solve these problems while avoiding the common pitfalls and errors that tend to pop up.

Now check out the video and see how to find the resultant force of a force system in the most efficient manner come your FE Exam day.

As always, we are here to help, Prepineer