# Force

force is a push or a pull applied by one object and experienced by another object.2 The net force on an object is the single force that could replace all the individual forces acting on an object and produce the same effect. Forces acting in the same direction add together to determine the net force; forces acting in opposite directions subtract to determine the net force.

Center of mass

The center of mass is the average distance, weighted by mass.

In a Cartesian coordinate, the center of mass is the point obtained by doing a weighted average for all the positions by their respective masses.2 The center of mass of the Earth and a chicken in space is going to be almost at the center of the Earth, because the chicken is tiny, and its coordinate is weighted so. The center of mass between two chickens in space is going to be right in the middle of the two chickens, because their positions are weighted equally. The absolute coordinates do not have to be obtained when calculating the center of mass. The point of reference can be set anywhere and relative coordinates used. The center of mass for a sphere is at the center of the sphere. The center of mass of a donut is at the center of the donut (the hole). The interesting thing about the center of mass of an object or system is that it is the point where any uniform force on the object acts. This is useful because it makes it easy to solve mechanics problems where we have to describe the motion of oddly-shaped objects and complicated systems.2 Together, these give the full coordinates of the center of mass of the system. For example, consider the system of three flat objects of uniform density shown below.

The center of mass in the x direction is:

1.4 + 1.5 + 2.12 = 8.5

1 + 1 + 2

And in the y direction:

1.5 + 1.12 + 2.85 = 8.5

1 + 1 + 2

Complex objects can often be represented as collections of simple shapes, each with uniform mass. We can then represent each component shape as a point mass located at the centroid. Voids within objects can even be accounted for by representing them as shapes with negative mass.

Newton’s first law, inertia

The law of inertia basically states the following: without an external force acting on an object, nothing will change about that object in terms of speed and direction.3 In the absence of an external force:

1. i) Something at rest will remain at rest
2. ii) Something in motion will remain in motion with the same speed and direction.

iii) Objects are inert to changes in speed and direction.

An example can be shown using centripetal force on a ball attached to a string. The string must provide the necessary centripetal force to move the ball in a circle.

If the string breaks, the ball will move off in a straight line. The straight line motion in the absence of the constraining force is an example of Newton’s first law. The example here presumes that no other net forces are acting, such as horizontal motion on a frictionless surface. The vertical circle is more involved.

Newton’s second law

A net force acting on an object will cause that object to accelerate in the direction of the net force.3 The equation for force is:

## F = ma

The unit for force is the Newton. N = kg·m/s2. Both force and acceleration are vectors because they have a direction.

Newton’s third law

This law states that every action has an equal and opposite reaction. For simple purposes, fields are lines.3 When lines are close together, that’s shows a strong field and when lines are far apart, that shows a weak field. Lines / fields have direction too, and as such, they are vectors. Things travel parallel, perpendicular, or spiral to the field line.

The boy is pulling the wall with 500N of force. However, the wall is also exerting 500N of force but in the opposite direction. Hence, neither the boy nor the wall is moving as the resultant net force is zero. Sometimes students have a difficulty grasping the concept of inanimate objects exerting force.3 In the second example, we see the boy once again exerting a force of 500N of force on the elephant. The elephant is also exerting a force of 500N of force, hence neither the boy nor the elephant is moving. If the boy was exerting more force than the elephant, then the elephant would move towards the boy and vice versa.

References

1) Kane, Thomas R.; Levinson, David A. (1996), Dynamics Online, Sunnyvale, California: Online Dynamics.    vectors

2) Resnick; Halliday; Krane (1992). Physics, Volume 1 (4th ed.). p. 83.

3) Beatty, Millard F. (2006), Principles of Engineering Mechanics, Volume 2: Dynamics—The Analysis of Motion, Mathematical Concepts and Methods in Science and Engineering, 33, Springer

4) Louis Bloomfield, Professor of Physics at the University of Virginia, How Everything Works: Making Physics Out of the Ordinary, John Wiley & Sons (2007)

5) Adkins, C.J. (1968/1983). Equilibrium Thermodynamics, third edition, McGraw-Hill, London

6) Jammer, Max (1957). Concepts of Force. Dover Publications, Inc. p. 167; footnote 14 work

7) C Hellingman (1992). “Newton’s third law revisited”. Phys. Educ. 27 (2): 112–115. Bibcode:1992 PhyEd..27.

8) Resnick & Halliday (1977). Physics (Third ed.). John Wiley & Sons. pp. 78–79. Any single force is only one aspect of a mutual interaction between two bodies.

9) Jain, Mahesh C. (2009). Textbook of Engineering Physics (Part I). p. 9. Chapter 1, p. 9

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