A force is a vector quantity that is it has both a magnitude and a direction. From Newton’s first law, a particle is said to be in equilibrium if the vector sum of all the forces acting on it is zero. (Young and Freeman, 2011, p.134). Using this statement any system of forces can be analysed. There are different types of system of forces namely coplanar, concurrent, coplanar concurrent and coplanar non-concurrent forces. The system of forces encountered in this experiment was the coplanar concurrent forces. Coplanar forces are forces with line of action on the same plane and concurrent forces are forces with line of action intersecting at the same point. (Hibbeler, R.C.,2010, p.170).
Aim: To verify the law of the polygon of concurrent forces
To understand the coplanar and concurrent systems of forces
To understand equilibrium of forces acting at a point
To show that for a system of coplanar concurrent forces to be in equilibrium, the force polygon is closed.
Importance of theory
This experiment of polygon of forces is important so as to prove if a system is in equilibrium or not. Using Newton’s first law of motion, the vector sum of the concurrent forces acting on a body is zero implying static equilibrium is reached.
Engineers can use polygon of forces to calculate force distribution which are crucial in structural design.
Knowing that the system is in static equilibrium that is the resultant force is zero, an unknown force, F’ can be found by closing the polygon with force F’. The length and direction of the line are used to find the force F’.
The law of polygon of forces states that if more than two forces act on a particle, they can be represented by consecutive sides of a polygon in order then the resultant force is obtained by the closing side of the polygon in reverse order.
There are two main types of methods to verify the law of polygon of concurrent forces: Analytical and graphical methods.
The analytical method is based on the component of the resultant force on an axis being equal to the sum of the component of the forces of the system on that same axis. (Szolga, I.V., 2010, p.18). If the system is in equilibrium, the components of the resultant force are equal to zero resulting in the following equations:
The graphical method is used to find the resultant force by drawing a polygon of forces. By using a scale, the length of each side of the polygon is determined by the magnitude of the force which is equal to the weight added at the end of each strings. The direction of each side of the polygon is determined by measuring the angle anticlockwise from a horizontal line. Each force is represented by an arrow and the first one starts at the origin. Then another force starts at the tip of the previous force. This continues until a closed polygon is formed. (Szolga, I.V., 2010, p.18). If the system is in equilibrium, a closed polygon should be obtained meaning that the resultant force is zero.
In some cases the polygons do not close, this is due to experimental error. Therefore the closing side of the polygon in reverse order represents the resultant force.
HIBBELER R.C.,2010. Engineering Mechanics Statics.12th ed.
YOUNG, H.D. AND FREEMAN, R.A.,2011. University Physics with Modern Physics. 13th ed.
SZOLGA, I.V., 2010. Theoretical Mechanics. online Available from: http://civile.utcb.ro/cmsdc/mechanics.pdf