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# Newton's Laws of Motion

Newtonian laws have become a handful in illustrating the relationship between forces and motions. The type of relationship that exists between the two is counter-intuitive and as such needs a careful review as well as an explanation. The first law suggests that a body will remain static or continue in its state of motion unless an external force acts upon it (F net = O). The second law, however, suggests that the same body will have an accelerated body which results from the net force acting on the body (F net = Ma). The third law, however, can be defined merely as action and reaction are equal and opposite (Kuehn, p. 261-264). Having established the three laws the one that best describes the purpose of this experiment is the second law of motion. The thesis of this problem will thus propose a way of checking the law as well as how it can be used to determine the relationship between motion and forces.

## Literature Review

The various researches conducted in the past have investigated the Magnus effects of Newton's laws of motion. These effects are closely associated with forces such as gravity, friction, and momentum. However, the studies have revolved around projectile motions especially the curving of the ball when kicked. According to Whitaker (p. 352) when an object is thrown upwards, it reaches an acceleration of zero at the maximum point where it changes direction due to the force of gravity. The study of motion is categorized into two from Bigland and Lippold (p. 224) point of view, and they include kinetics which illustrates how objects move and dynamics which describes the involvement of the force. The two categories are also determined by the forces that bring about Magnus effects. The normal force differs from the applied force due to the addition of the friction force and thus Fn = Fapp – Coefficient of Friction (Bigland and Lippold, 214-224).

## Results

To investigate the thesis, four experiments were conducted and which yielded different results. The first experiment was to examine the relationship between mass and the magnitude of the normal force between different objects using the formula Fn = mg. From table 1 (see Appendix) it is determined that Fn differs between objects of different masses, for example, Quartz had an Fn = 87.612N while Ruby had Fn = 132.3N. This means that mass is the determinant factor since gravitational force is constant. The second force, on the other hand, was to determine the coefficient of the static friction of the same objects using µk = Fapp/Fn. The results of the calculation are as indicated in table 2 (see Appendix) and differ between the objects. The difference in the values is as a result of the mass between each cube. Since force is applied, motion occurs and this type of motion is described as accelerated because the force applied is higher than the static friction maximum. The latter is illustrated by graph 1 (see Appendix).

The third experiment involved the investigation of the kinetic friction coefficient, and as indicated in experiment two it differs among the cubes (Table 3 in the Appendix). It is also observed that the coefficients of the static motion are higher than that of kinetic friction. This is illustrated by the first and second Newtonian laws of motions since the force required to start motion is greater than that needed to keep it in motion. This relationship can be described using graph 2 available in the Appendix. The last activity, however, introduces acceleration to the previous experiment, and it is observed that the kinetic coefficient of friction is constant (see Table 4 in the appendix). The relationship between velocity and time is found to be linear (Graph 3 in the Appendix).

## Conclusion

The results from the experiment indicate that mass plays a significant role in determining variables such as acceleration, mass, applied force as well as the normal force. The relationship between the three values can also be calculated using the Newtonian laws of motion. These laws dictate the type of motion and how they differ between different objects.

## Work Cited

Bigland, Brenda, and O. C. J. Lippold. "The relation between force, velocity and integrated electrical activity in human muscles." The Journal of physiology 123.1 (1954): 214-224.

Giancoli, D.C. (1998). Physics: principles with applications. 5th ed. Englewood Cliffs, NJ: Prentice Hall.

Kuehn, Kerry. "Newton’s Laws of Motion." A Student's Guide Through the Great Physics Texts. Springer, New York, NY, 2015. 261-264.

Whitaker, Robert J. "Aristotle is not dead: Student understanding of trajectory motion." American Journal of Physics 51.4 (1983): 352-357.

Appendix

Table 1: Mass and Magnitude of Normal Force

Cube

Mass

(kg)

Magnitude of Normal Force (N)

Quartz

8.94

87.612

Ruby

13.5

132.3

Aluminum

9.11

89.278

Gold

65.14

638.372

Table 2: Coefficient of Static Friction

Cube

Magnitude of Normal Force

(N)

Magnitude of

Applied Force

(N)

Static Coefficient

of

Friction

Quartz

87.612

28.90

0.32986349 μk

Ruby

132.3

26.50

0.20030234 μk

Aluminum

89.278

36.60

0.40995542 μk

Gold

638.372

44.70

0.07002187 μk

Table 3: Coefficient of Kinetic Friction Data 2

Cube

Magnitude of

Normal Force

(N)

Magnitude of

Applied Force

(N)

Kinetic Coefficient

of

Friction

Quartz

87.612

19.30

0.22028946

Ruby

132.3

19.90

0.15041572

Aluminum

89.278

24.10

0.26994332

Gold

638.372

31.90

0.04997086

Table 4: Coefficient of Kinetic Friction Data 3

Cube

Magnitude of

Normal Force

(N)

Magnitude of

Applied Force

(N)

Acceleration

(m/s2)

Kinetic Coefficient

of

Friction

Quartz

87.612

45

2.875

0.22026092

Ruby

132.3

45

1.859

0.15044218

Aluminum

89.278

45

2.294

0.26996192

Gold

638.372

45

0.197

0.05038977

Graph 1: Velocity vs Time (Coefficient of Static Friction)

Graph 2: Velocity vs Time (Coefficient of Kinetic Friction Data 2)

Graph 3: Velocity vs Time (Coefficient of Kinetic Friction Data 3)