Force systems

Today we are going to study how the forces acting on the same body can be, that is, we are going to study the systems of forces; since they are the set of forces that act on a body at the same time.
Each of the forces that make up the force system is called a component of the system. We call the resultant a single force whose result is the same as that produced by the entire set of forces in the system. Similarly, we call equilibrium the force whose modulus is equal to the resultant but is in the opposite direction.
In the following image we can see two components F1 and F2 that act on the body A, and whose resultant is R.

To calculate the resultant (R) we represent the second force F2 by making the end of F1 coincide with the origin of F2, parallel to our initial F2; as we can see in the previous image. The result will be the vector that joins the origin of the first force, that is, where our body (A) is located, with the end of F2.
Next we are going to see the different systems of forces that we can find as the forces on the bodies appear.

FORCES ACTING IN THE SAME SENSE
When two forces with the same sense act on our body, the intensity of the resulting force will be the sum of the intensities of the forces, and will have the same meaning as them.
Example: Find the resultant of the following components: F1 = 5N and F2 = 3N, which act by pushing the body to the right.
The result will be: R = 5N + 3N = 8N and the sense of force will also be to the right, as we can see in the following image.

FORCES ACTING IN OPPOSITE SENSES
If two forces act on a body, they have opposite senses, that is, while one goes to the right, the other direction is to the left; then the intensity of the resultant is obtained by subtracting the intensities of the forces. While the sense of the resultant coincides with the sense of force with greater intensity.

Example: Given the forces F1 = 10N and F2 = 4N, in such a way that the first goes to the right and the second to the left, obtain the resulting force:
To calculate the resultant we perform the following subtraction: R = 10N-4N = 6N. The direction of the resultant will coincide with the direction of the first force, therefore, to the right.

ANGULAR FORCES
When two forces act on the same body in such a way that their directions form an angle, we say that the forces are angular.
To calculate the result, we use what we have commented at the beginning of the article.

PARALLEL FORCES IN THE SAME SENSE
When two forces act in parallel and in the same direction, the intensity of the resultant is calculated by summing the intensities of the components. And it will have the same meaning as both forces. Finally, the application point will be a point in between such that F1xd1 = F2xd2, being closer to the force of greater intensity.

Example: Let the forces F1 = 12N and F2 = 9N be 14 cm apart. Calculate the resulting force and its point of application.
The intensity of the resultant will be: R = F1 + F2 = 12N + 9N = 21N The point of application will be the solution of the system formed by these two equations: 12d1 = 9d2 and d1 + d2 = 14. So d1 = 6, that is, the application point is 6cm from F1.


OPERATIVE PARALLEL FORCES

When two forces act in parallel and in the opposite direction, the intensity of the resultant is calculated by making the difference of the intensities of the components. It will have the direction of the component with the highest intensity and the application point is calculated as in the previous case.

Example: Let the forces F1 = 12N and F2 = 20N, in such a way that F1 goes up and F2 down, calculates the intensity of the resultant and its point of application. In such a way that they are 10cm apart.
The intensity will be R = F2 – F1 = 20N – 12N = 8N.
The direction will be downwards since the one with the highest intensity is F2.

The application point, as in the previous case, will be obtained by calculating the system formed by the following equations: 12d1 = 20d2 and d1-d2 = 10.

 

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