Newton's third law and Mass & Weight | POINT classical mechanics

 Newton's third law and Mass & Weight

In the realm of classical mechanics, the intricate relationship between force interactions and the inherent properties of matter offers a window into the workings of the physical world. Newton's third law brings to light the reciprocal nature of forces, emphasizing that interactions occur in balanced pairs. Alongside this, the concepts of mass and weight, while often mentioned together in everyday language, reveal distinct characteristics when viewed through a scientific lens. This discussion delves into how the interplay between reciprocal forces and the differences between mass and weight enriches our understanding of motion and matter.

Newton's third law

To understand Newton's Third Law, we can use the following daily life observations: 

When a person sitting in a wheelchair is pushed against a wall (the first force), the chair is pushed backwards (the second force). 

When a shell is fired from a gun forward (the first force), the gun recoils backwards (the second force), so the soldier fixes the gun butt in the shoulder cavity. 

When a balloon is inflated and then released, the air rushes out of it in a certain direction (the first force) and the balloon rushes in the opposite direction (the second force).

From the above, we conclude that Newton's third law is related to two mutual forces between two different bodies. If we consider the first force (F1) as an action, then the second force (F2) as a reaction and is equal to the first force and in the opposite direction. From here, we can deduce the text of Newton's third law: 

 

- Newton's third law: when a body affects another body with a force, the second body affects the first body with a force equal to it in magnitude and opposite to it in direction. 

or

For every action, there is a reaction equal in magnitude and opposite to it in direction. 

The mathematical formula for Newton's third law: F1 - F2

The negative sign means that the two forces are in opposite directions.

*There is no single force in the universe because the forces of action and reaction arise together and disappear together. 

*The forces of action and reaction, despite their equality, do not create equilibrium (the resultant of action and reaction ≠ zero) because the two forces affect two different bodies and the condition for equilibrium is that the two forces affect one body. 

*The action and reaction have the same nature, so if the action is a gravitational force, then the reaction is also a gravitational force.

Practical application

The idea of ​​how a rocket works depends on Newton's third law because the thrust of a huge mass of burning gases from below the rocket makes it thrust upwards due to the force of reaction

Mass & Weight

The concept of mass (m) differs from the concept of weight (w), and the following table shows the comparison between them in terms of:

Concept-Type of physical quantity-Mathematical relationship-Unit of measurement-Formula of dimensions-Effect of place
(in order)

1- mass
The amount of resistance of the body to any change in its transitional state of motion
Basic standard quantity
m = F/a
Kilogram (kg)
M
Constant no matter how the place changes


2 weight
The force of gravity on the body
A derived quantity directed towards the center of the Earth
w = mg
Newton (N)
M.L/T²
Changes with the change in the acceleration of gravity from one place to another

*The weight of the astronaut on the surface of the moon differs from that on the surface of the earth,

*Because the acceleration due to gravity on the surface of the moon differs from that on the surface of the earth.

*The weight of the body changes from one place to another on the surface of the earth
Because the acceleration due to gravity changes slightly from one place to another on the surface of the earth (w = mg).

If you want to continue reading about circular motion

Reflecting on the dynamics explored, the combined insights of reciprocal force interactions and the nuanced distinction between mass and weight underscore the elegance of classical mechanics. By appreciating how every force has its counterforce and recognizing the subtle differences in how we perceive matter, we gain a deeper understanding of the physical principles that govern our universe. This integrated perspective not only enhances our theoretical grasp of the subject but also informs practical applications in technology and engineering, reinforcing the timeless relevance of these core concepts in our continuous exploration of nature.