Illusion of Force and Mass

Let us start with the famous Newton’s second law of motion.

F = ma

   where

   F- net force acting on the body

   m- mass of the body

   a- acceleration of the body

What is the mass of a body? Generally, mass is attributed to the amount of matter in a body. How do we measure the mass of any body? Due to the unique property of gravitational force, on Earth’s surface weight (mg) of any body is proportional to mass. Dividing weight by constant g, the mass of a body can be obtained. While from the second law of Newton, we calculate force given the mass and acceleration, for measuring mass itself it is required to use some kind of force. This makes equation F=ma look like a cyclic illusion.

Even though we cannot measure mass directly without using some force, there is a way to verify the above equation. Let's say first we take a solid iron block and assume its mass to be m. We apply force F on it which results in the acceleration of the block. Now we brake the block into two halves. Assuming the mass of each resulting sub-block is m/2. We apply the same F force on the resulting block of mass m/2. Then we break this block into another two. Applied force F on the block of mass m/4. The acceleration for m/2 and m/4 should be 2a and 4a for the same force. Thus we can verify Newton's second equation by the method of cutting a standard block into pieces. Here it was assumed that mass is proportional to the volume of the body, as the block that is broken into two halves must have twice the matter than every two broken parts.

The important thing to note about equation F=ma is that force as such does not need to be defined by mass. There are four fundamental forces in nature 1. strong nuclear 2. weak nuclear 3. Electromagnetic 4. Gravitational. Force acting can be any one of them or derived from them. The consequence of this force on the body is acceleration which is related by the above equation. Where mass m is the intrinsic property of the body which decides how much acceleration will be generated for the given force. As seen in the previous example of a block, it is related to the amount of matter in a body but as such without force, there is no way to define mass.

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