The resultant force is the sum of all the forces that act on the same body. When a body or object is subjected to the action of several forces simultaneously, an effect occurs. Acting forces can be replaced by a single force that produces the same effect. This only force is the resultant force also known as net force and is represented by the symbol F R .
The effect produced by F R will depend on its size, direction and direction. Physical quantities that have direction and sense are vector quantities.
Resulting forces. By Ilevanat (https://commons.wikimedia.org/wiki/File:Rezultanta.JPG), from Wikimedia Commons
As the forces acting on a body are vector magnitudes, the resultant force F R is a vector sum of all the forces and can be represented graphically with an arrow that indicates its direction and direction.
With the resultant force, the problem of a body affected by several forces is simplified by reducing it to a single acting force.
Formula
The mathematical representation of the resultant force is a vector summation of the forces.
F R = ∑ F (1)
∑ F = F 1 + F 2 + F 3 +… F N (2)
F R = Resulting force
∑ F = Sum of Forces
Note that the resultant force of expression (6) is not highlighted in bold type and it is because it only expresses the numerical value. The direction is determined by the angle θ x.
Expression (6) is valid for forces acting in the same plane. When forces act in space, the z-component of the force is taken into account when working with rectangular components.
Solved exercises
All the x and y components of the forces acting on the body are determined. The force F 1 has only one horizontal component on the x axis. The force F 2 has two components F 2x and F 2y that are obtained from the sine and cosine functions of the angle 30 °.
F 1x = F 1 = 70N
F 2x = F 2 cos 30 ° = 40 N.cos 30 ° = 34.64N
F 1y = 0
F 2y = F 2 sin 30 ° = 40 sin 30 ° = 20N
∑ F x = 70N + 34.64N = 104.64N
∑ F y = 20N + 0 = 20N
Once the resulting forces on the x and y axis have been determined, we proceed to obtain the numerical value of the resultant force.
F R 2 = (∑ F x) 2 + (∑ F y) 2
The resultant force is the square root of the sum of the squared components of the forces
F R = √ (104.64N) 2 + (20N) 2
F R = 106.53N
The angle formed by the resultant force F R is obtained from the following expression:
θ x = tan -1 (∑ F y / ∑ F x)
θ x = tan -1 (20N / 104.64N) = 10.82 °
The resultant force F R has a magnitude of 106.53N and has a direction determined by the angle of 10.82 ° it makes with the horizontal.
References
- Dola, G, Duffy, M and Percival, A. Physics. Spain: Heinemann, 2003.
- Avison, J H. The world of Physics. India: Thomas Nelson and Sons, 1989.
- Pinsent, M. Physical Processes. United Kingdom: Nelson Thomas, 2002.
- Yadav, S K. Engineering Mechanics. Delhi: Discovery Publishing House, 2006.
- Serway, RA and Jewett, J W. Physics for Scientists and Engineers. California, USA: Brooks / Cole, 2010.