This lab is aimed at studying the composition and equilibrium of coplanar forces. Additionally, the lab will also evaluate the rectangular resolution and the equilibrium of coplanar forces.

Theory

Part I: Comparison and equilibrium of coplanar forces

This part of the lab will demonstrate how several forces with their lines of actions lying on the same plane going through one point can be easily balanced by a single force that has a line of action going through the same point. This method will be used in the determination of this force known as the resultant. The magnitude of the resultant is the same as the original forces. The result will then be balanced by an equal opposite force known as the equilibrant. The resultant is determined using the method of vector addition. Three forces, i.e. F1, F2 and F3 acting on an object and passing through point O as illustrated in the figure below.

Figure 1: F1, F2 and F3 acting through point O

The resultant of the forces will be determined by the addition of the tip-to-tail method resulting polygons. The resultant in this case is the vector that connects the tail of the first vector with the head of the last vector. As illustrated below

Figure 2: The resultant using the polygon method

Part II: Rectangular resolution and equilibrium of coplanar forces

The principal objective of the experiment will be to illustrate that a single force can be resolved into two mutually perpendicular components that will be considered as equivalent to the given force. Figure 3 illustrates force F that can be resolved into mutually perpendicular forces x-axis and y-axis. The combined effect of Fx and Fy along their respective planes will be equal to force F.

Figure 3: The Rectangular resolution of force F

The sum of all the x-forces will form the x-component of the force while the sum of all the y-forces will form the y-component of the resultant.

Data

Part I

Theoretical Values for the Forces

X component

Y component

F1

76.60 g

64.27 g

F2

77.13 g

91.93 g

F3

70.71 g

84.26 g

Table 1: The theoretical x and y components of the forces

X component

Y component

F1

76 g

65 g

F2

83 g

100 g

F3

70 g

85 g

Table 2: The experimental x and y components of the forces

Fx component

Fy component

F1

-71.24 g

71.94 g

Table 4: The theoretical Fx and Fy components of the forces for the sum of all components

Fx component

Fy component

F1

77 g

80 g

Table 4: The experimental Fx and Fy components of the forces for the sum of all components

Sample Calculation

Using trigonometry to compute the components

Components of F1

Components of F2

Components of F3

Error Computation

For the summation of the angle

Graphs

Figure 4: The Space diagram

Figure 5: The force diagram

Figure 6: The rectangular resolution of the forces

Figure 7: The equilibrium of the coplanar force

Answer to questions

Question one

The displacement of the ring means that the net force of the system will no longer be zero. This displacement will mean that there is a change in the magnitude of the forces or the net direction of the forces or both.

Question Two

Condition 1: The sum of all the magnitude of the forces in all direction must be equal to zero. Thus the net force on the object will be equal to zero.

Condition 2: The sum of all the rotational forces is equal to zero. The object, in this case, will not rotate.

Conclusion

Finally, the experiment has illustrated that if the forces acting on an object cancel out then resultant net force will be zero and the object will static with no movement or rotation. It is also evident that using the components of a force we can resolve the magnitude and direction of a force. The resolution of these forces will result in zero and ultimately balance out.

Reference

Özkaya, N., Leger, D., Goldsheyder, D., " Nordin, M. (2016). Fundamentals of biomechanics: equilibrium, motion, and deformation. Springer.