PRINCIPLE OF TRANSMISSIBILITY OF FORCES (SOLVED EXERCISES) - PHYSICAL - 2025

The principle of transmissibility of forces indicates that the equilibrium or motion situation of a rigid body does not change if a certain force acting on a specific point on the body is replaced by another. For this to be considered this way, two premises must be met.

The first premise is that the new force is of the same magnitude, and the second is that the same direction is applied, even if it is on a different point on the body. The two forces have the same result on a rigid body; therefore, they are equivalent forces.

Thus, the principle of transmissibility confirms that a force can be transmitted along the same direction. Similarly, it should be noted that the mechanical effect of the force can be both rotational and translational. A practical example of the meaning of the principle of transmissibility is when a body is pushed or pulled.

If the value of the force with which the body is pulled or pushed is the same, and both forces are applied in the same direction, the resulting motion is exactly the same. Thus, for the purposes of movement, the result is the same, whether the body is pushed or pulled.

Rigid bodies

A rigid body (that does not deform) is any body that does not undergo deformations when an external force is applied to it.

The idea of ​​a rigid body is still a mathematical idealization necessary for the study of movement and the causes of the movement of bodies.

A more precise definition of a rigid body is what defines it as a system of material points, in which the distance between the different points of the body is not modified by the action of a system of forces.

The truth is that real bodies and machines are never completely rigid and experience deformations, even minimally, under the action of the forces and loads that are applied to them.

Limitations of the principle of transmissibility

The principle of transmissibility has some limitations. The first and most obvious is in the case that the applied force or forces act on a deformable body. In that case, the deformation of the body will be different depending on the point of application of the forces.

Another limitation is what can be seen in the following case. Suppose two forces applied horizontally on the ends of a body, both in the same direction but in the opposite direction.

According to the principle of transmissibility, the two forces could be replaced by two new forces applied in the same direction, but in opposite directions to the original ones.

For internal purposes, the substitution would have no consequence. However, for an outside observer, a fundamental change would have occurred: in one case the applied forces would be tension, and in another they would be understanding.

Therefore, it is clear that the principle of transmissibility is only applicable from the hypothesis of its application to ideal rigid solids and from the perspective of an internal observer.

Examples

First example

A practical case of application of the principle of transmissibility occurs when you want to move a car by a group of people.

The car will move in the same way whether it is pushed or pulled forward, as long as people apply force in the same straight line.

Second example

Another simple example in which the principle of transmissibility is fulfilled is that of the pulley. For the purpose of movement, the point on the string to which the force is applied is indifferent, as long as the same amount of force is applied. In this way, it does not affect the movement if the rope is more or less long.

Solved exercises

Exercise 1

Indicate whether the principle of transferability is met in the following cases:

First case

A force of 20 N applied horizontally on a rigid body is replaced by another force of 15 N applied at another point on the body, although both are applied in the same direction.

Solution

In this case, the principle of transmissibility will not be fulfilled since, although the two forces are applied in the same direction, the second force does not have the same magnitude as the first. Therefore, one of the indispensable conditions of the principle of transmissibility does not exist.

Second case

A force of 20 N applied horizontally on a rigid body is replaced by another also of 20 N, applied at another point on the body and vertically.

Solution

On this occasion, the principle of transmissibility is not fulfilled since, although the two forces have the same modulus, they are not applied in the same direction. Again, one of the indispensable conditions of the principle of transmissibility does not exist. It can be said that the two forces are equivalent.

Third case

A force of 10 N applied horizontally on a rigid body is exchanged for another also of 10 N applied at another point on the body, but in the same direction and direction.

Solution

In this case, the principle of transmissibility is fulfilled, since the two forces are of the same magnitude and are applied in the same direction and direction. All the necessary conditions of the principle of transmissibility are fulfilled. It can be said that the two forces are equivalent.

Fourth case

A force slides in the direction of your line of action.

Solution

In this case, the principle of transmissibility is fulfilled since, being the same force, the magnitude of the applied force does not vary and it slides in its line of action. Again all the necessary conditions of the principle of transmissibility are fulfilled.

Exercise 2

Two external forces are applied to a rigid body. The two forces are applied in the same direction and in the same direction. If the modulus of the first is 15 N and that of the second is 25 N, what conditions must a third external force that replace the resultant of the two previous ones meet to fulfill the principle of transmissibility?

Solution

On the one hand, the value of the resultant force has to be 40 N, which is the result of adding the modulus of the two forces.

On the other hand, the resultant force must act at any point on the straight line joining the two points of application of the two forces.

References

1. Rigid body (nd). In Wikipedia. Retrieved on April 25, 2018, from es.wikipedia.org.
2. Force (nd). In Wikipedia. Retrieved on April 25, 2018, from en.wikipedia.org.
3. Cutnell, John D.; Johnson, Kenneth W. (2003). Physics, Sixth Edition. Hoboken, New Jersey: John Wiley & Sons Inc.
4. Corben, HC; Philip Stehle (1994). Classical Mechanics. New York: Dover publications.
5. Feynman, Richard P.; Leighton; Sands, Matthew (2010). The Feynman lectures on physics. Vol. I: Mainly mechanics, radiation and heat (New millennium ed.). New York: BasicBooks.