Force
Composition of Forces
Net force (also known as resultant force) is the overall force acting on an object when all the individual forces acting on the object are added together.
The net force is a vector produced when two or more forces act on a single object. It is calculated by vector addition of the force vectors acting on the object.
The result of adding two or more forces is called resultant force13.
Forces acting in one line
Forces acting in one line can be added by algebraic sum.
To understand force vector adding, we will begin with forces acting in one line.
Example
A coach is assisting his charge in bench press with a barbell of 100 kg. The coach is acting on the barbell with the force of 70 N and the athlete with the force of 920 N in upward direction. Will they manage to lift the barbell? What is the resultant force acting on the barbell?
Solution:
Weight force of the barbell can be calculated as:
FG = mg = 100 ⋅ 9,81 = 981 N.
Let us assume that upward direction of the force is a positive direction, therefore:
F = 70 N + 920 N + (−981 N) = 9 N.
The resultant force F is 9 N and the athlete, with a little help from his coach, will manage to lift the barbell.
Concurrent Forces
Concurrent forces do not act in one line but they all pass through a common point (Fig. 2).
Figure 2 Adding concurrent forces.
Resultant force vector is the diagonal of the rectangle created by both horizontal and vertical force and their parallel lines. Resultant force can also be described by the angle between the resultant force and either the vertical or horizontal line.
Trigonometric Technique
We can arrive at the same result making us of the Pythagoras’ theorem. In principle, trigonometry studies triangles and the relationships between their sides and the angles between these sides.
Example
Vertical reaction force of the Earth (normal contact force), acting on a runner’s foot, has the magnitude of FRA = 2200 N; friction force is acting backward and its magnitude is FRB = 500 N. What is the direction and the magnitude of the resultant force FRC (Fig. 3)?
Figure 3 Landing in running. The blue arrow represents the resultant reaction force FRC. Black arrows represent friction component of the reaction force FRB and vertical component of the reaction force FRA, respectively, both acting on the foot.
To calculate the resultant force, we will use the Pythagoras’ theorem:
FRA2 + FRB2 = FRC2
FRC2 = 22002 + 5002
FRC = 2256 N.
and arctangent function to calculate the angle between the resultant and the horizontal force:
The magnitude of the resultant force FRC is 2256 N and its angle with horizontal line is α = 77,2°.
The magnitude of the resultant force from two perpendicular forces can be calculated with the use of the Pythagoras’ theorem, its direction can be calculated with the use of trigonometry.
13 In English literature the term „net force“ can also be found, representing vector addition of the force vectors acting on an object.Zpět