Principle of Transmissibility of Forces (with Exercises Resolved)

He principle of transmissibility of forces indicates that the situation of balance or movement of a rigid body does not change if a certain force acting on a particular point of the body is replaced by another. For this to be considered, two premises must be fulfilled.

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 of the body. The two forces have the same result on a rigid body; therefore, they are equivalent forces.

Principle of transmissibility of forces

Thus, the principle of transmissibility confirms that a force can be transmitted along the same direction. Similarly, it is convenient to emphasize that the mechanical effect of force can be both rotation and translation. A practical example of the meaning of the principle of transmissibility is given 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 movement is exactly the same. Thus, for the purpose of movement the result is the same, push or pull the body.

Index

  • 1 Rigid bodies
  • 2 Limitations of the principle of transmissibility
  • 3 Examples
    • 3.1 First example
    • 3.2 Second example
  • 4 Solved exercises
    • 4.1 Exercise 1
    • 4.2 Exercise 2
  • 5 References

Rigid bodies

It is called a rigid body (that does not deform) to any body that does not suffer deformations when an external force is applied on it.

The idea of ​​rigid body does not cease to be a mathematical idealization necessary for the study of movement and the causes of the movement of bodies.

A more precise definition of 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 charges applied to them.

Limitations of the principle of transmissibility

The principle of transmissibility presents some limitations. The first and most obvious is in the case that the force or forces applied 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 the one that 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 external observer a fundamental change would have taken place: in one case the applied forces would be of tension, and in another they would be of 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 applying the principle of transmissibility occurs when you want to move a car for a group of people.

The car will move in the same way whether they push it or pull it forward, as long as people apply force on the same straight line.

Second example

Another simple example in which the principle of transmissibility is met is that of the pulley. For the purpose of movement, the point of the rope on 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 string is more or less extensive.

Principle of transmissibility of forces 1

Solved exercises

Exercise 1

Indicate whether the principle of transmissibility is fulfilled in the following cases:

First case

A force of 20 N applied horizontally on a rigid body by another force of 15 N applied at another point of the body is substituted, although both apply 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 is not met.

Second case

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

Solution

On this occasion, the principle of transmissibility is not fulfilled since, although the two forces have the same module, they do not apply in the same direction. Again, one of the indispensable conditions of the principle of transmissibility is not met. It can be affirmed that the two forces are equivalent.

Third case

A force of 10 N applied horizontally on a rigid body by another also of 10 N applied at another point of the body, but on the same direction and sense.

Solution

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

Fourth case

A force slides in the direction of its action line.

Solution

In this case the principle of transmissibility is fulfilled given that, being the same force, the magnitude of the applied force does not change and it slips in its line of action. Once 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 module of the first one is 15 N and that of the second one of 25 N, what conditions must a third external force that replaces the one resulting from the two previous ones fulfill the principle of transmissibility?

Solution

On the one hand, the value of the resulting force must 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 of the straight line joining the two points of application of the two forces.

References

  1. Rigid body (n.d.). In Wikipedia. Retrieved on April 25, 2018, from es.wikipedia.org.
  2. Force (n.d.). 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, H.C.; 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.