Characteristics of a Force (Principle of Transmissibility)

Characteristics of a Force (Principle of Transmissibility)

• Every force is characterized by its magnitude, direction and point of application. The direction and point of application together define its line of action. When force is applied on an object, it can produce motion of the object and deformation. 

• When translational motion of an object is being studied, the point of application of force can be changed without causing any change in the acceleration of the object. 

Note: The force has to be treated as a free vector while studying the translational motion of objects.

• Example: For an object of mass 5 kg as shown in Fig. 1.9.1 (a), the acceleration produced by a 10 N horizontal force acting at A will be 2 m/s2 towards right.

• The same acceleration is obtained if the force is shifted to point B as shown in Fig. 1.9.1 (b).

• While studying rotational motion of an object, changes in point of application can change the moment produced by that force.

• If a force F acting at point A is shifted to another point B on its line of action, the perpendicular distance from any point O will remain the same as shown in Fig. 1.9.2 (a).

• Therefore the moment of force remains same in magnitude and sanse of rotation even if the force is transmitted to any point on line 'aa'.

• Hence the angular acceleration produced by the force would remain the same even if the force is shifted to any point of the line 'aa'.

• As discussed earlier, the linear acceleration is also same for such a shift in the point of application of force.

• If the force is shifted to some point 'C' which is not on the line 'aa', then the perpendicular distance from point "O' changes. This will change the go left moment of force about 'O'. As a result, the angular acceleration will change even though the linear acceleration will remain same.

• Thus, the motion of object remains unchanged even if the force is transmitted from one point to another on its line of action i.e., the force can be considered as a sliding vector. This statement is called the law of transmissibility of force. 

• When deformations of objects are studied due to forces, the forces must be considered as fixed vectors, i.e., their point of application cannot be changed.

• If transmissibility is used, a compressive force system can change to tensile or vice versa. Consider a rod acted upon by two equal and opposite axial forces as shown in Fig. 1.9.3. For the points of application of the two forces in Fig. 1.9.3 (a), the rod will get compressed, in Fig. 1.9.3 (b), the rod will be elongated and in Fig. 1.9.3 (c), there will be no change in dimensions.

• All these three cases are however equivalent with respect to their motion as the resultant force in all the cases is zero.