Understanding the Fundamentals: Breaking Down Forces Into Their Components

In many problems, forces act in various directions. DO NOT let this overwhelm you. If you simplify the angled force(s) into its components (x- and y-), you can use them to form a right triangle.

Each problem usually states an angle and a direction. I use my “Vegas Chart” to put all the x-components of the forces in one column and the y-components of the forces in a second column. This will allow us to take any number of forces, find their horizontal and vertical components, and combine them to find the overall net force with the Pythagorean Theorem and simple right angle trigonometry. Don’t worry, there is no need for the unit circle. 

Breaking these forces into components makes finding the net force acting on the block easier.

Steps for Solving Summation of Forces Problems:

1. Draw a free-body diagram (FBD): Represent each force with an arrow, showing the direction and relative magnitude. This visual is crucial for organizing information and solving the problem.

2. Draw a Vegas Chart with an x-column and a y-column

3. Break down the forces into their x- and y- components and put them in the appropriate column.

4. Add up the forces in each column to get an overall force in the x-direction and an overall force in the y-direction.

5. Use the two overall forces in step 4 to draw a right triangle

6. Use the Pythagorean Theorem and Sohcahtoa to find the resulting force vector.

If you need more help understanding these concepts, schedule an appointment by contacting me at Kevin@doyletutor.com.