Modern Physics

# Principle of Transmissibility of Force (Resolved Exercises)

The principle of transmissibility of forces indicates that the balance or movement of a rigid body does not change if a certain force acting at a specific point on the body is replaced by another. For this to be considered, 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 at a different point on the body. The two forces have the same result in a rigid body; therefore, they are equivalent forces.

Thus, the principle of transmissibility confirms that a force can be transmitted in the same direction. Likewise, it should be noted that the mechanical effect of 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 amount of force with which the body is pulled or pushed is the same, and the two forces are applied in the same direction, the resulting movement will be exactly the same. So, for movement purposes, the result is the same, push or pull the body.

## rigid bodies

It is called a rigid (non-deforming) body for any body that does not deform 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 different points on 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 suffer deformations, even minimally, under the action of forces and loads applied to them.

## Limitations of the principle of transferability

The principle of transferability has some limitations. The first and most obvious is that the applied forces act on a deformable body. In this 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 at the ends of a body, both in the same direction but in the opposite direction.

According to the transmissibility principle, 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 replacement would have no consequences. However, for an external observer, there would be a fundamental change: 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 applicable only from the assumption of its application to ideal rigid solids and from the perspective of an internal observer.

## Examples

### first example

A practical case of applying the transferability principle is when you want to move a car for a group of people.

The car will travel in the same way, pushing or pulling forward, as long as people apply force in the same straight line.

### second example

Another simple example where the transferability principle is fulfilled is the pulley. For movement purposes, the point on the cable to which force is applied is immaterial, as long as the same amount of force is applied. This way, it doesn’t affect the movement if the string is more or less long.

## solved exercises

### Exercise 1

Indicate whether the principle of transferability is complied with in the following cases:

#### first case

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

##### Solution

In this case, the transmissibility principle 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 20 N force applied horizontally to a rigid body is replaced by another 20 N force applied elsewhere on the body and vertically.

##### Solution

This time, the principle of transmissibility is not fulfilled, since, although the two forces have the same magnitude, 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 10 N force applied horizontally on a rigid body is exchanged for another 10 N force applied elsewhere 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 necessary conditions of the transferability principle are fulfilled. It can be said that the two forces are equivalent.

#### fourth case

A force slides towards its 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 slides in its line of action. Again, all necessary conditions of the transferability principle 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 the second is 25 N, what conditions must be met by a third external force that replaces the result of the previous two in order to comply with the transmissibility principle?

#### Solution

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

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