prove that Newton's second law of motion is the real law of motion
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First law is contained in second law: According to Newton’s second law of motion,
F=ma
It means that there will be no acceleration in the body if no external force is applied. This represents that a body at rest will remain at rest and a body in uniform motion will continue to move along the same straight line in the absence of an external force. This corresponds to Newton’s first law of motion. So, first law of motion is contained in Second law of motion
F=ma
It means that there will be no acceleration in the body if no external force is applied. This represents that a body at rest will remain at rest and a body in uniform motion will continue to move along the same straight line in the absence of an external force. This corresponds to Newton’s first law of motion. So, first law of motion is contained in Second law of motion
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Nothing in physics can be proven in the mathematical sense. Sometimes mathematical physicists begin with axioms that are thought to model an aspect of the natural world and then work out what follows from these axioms. Their derivations are proofs in the mathematical sense of what follows from the axioms, but ultimately they do not prove anything about the natural world. If their proofs fail to reflect observed reality, however, we can say (contrapositively) that at least one of the beginning axioms must be untrue.
An example of such theorems (in this special sense of the word) is the spin statistics theorem.
Newton's law on the other hand is more of a definition made to describe our experience. Beginning with Newton's first law, that something's state of motion does not vary with time unless it interactswith something else, we seek to describe more precisely the case where there is such interaction and therefore a change in motion state. It is natural to say that the more the first law is violated, the stronger must be the "interaction". We also witness that the same causative agent of such a "violation" (e.g. a stretched spring) affects different bodies differently. Bodies that are "more massive" in some way are affected less than "less massive" ones.
So one can encode these qualitative, but accurate, descriptions in a definition F⃗ =dt(mv⃗ )F→=dt(mv→). So F⃗ F→, by definition, encodes the "strength" of the interaction that begets a change dtdt of state of motion mv⃗ mv→. The stronger the interaction, the swifter the deviation from the First-Law-foretold motion. The constant of proportionality mm quantifies how different things react to the same causative agents: if something's acceleration is twice as much as that of something else under the influence of the same causative agent (e.g. the same stretched spring), then we say by definition that the latter is twice as massive as the former.
An example of such theorems (in this special sense of the word) is the spin statistics theorem.
Newton's law on the other hand is more of a definition made to describe our experience. Beginning with Newton's first law, that something's state of motion does not vary with time unless it interactswith something else, we seek to describe more precisely the case where there is such interaction and therefore a change in motion state. It is natural to say that the more the first law is violated, the stronger must be the "interaction". We also witness that the same causative agent of such a "violation" (e.g. a stretched spring) affects different bodies differently. Bodies that are "more massive" in some way are affected less than "less massive" ones.
So one can encode these qualitative, but accurate, descriptions in a definition F⃗ =dt(mv⃗ )F→=dt(mv→). So F⃗ F→, by definition, encodes the "strength" of the interaction that begets a change dtdt of state of motion mv⃗ mv→. The stronger the interaction, the swifter the deviation from the First-Law-foretold motion. The constant of proportionality mm quantifies how different things react to the same causative agents: if something's acceleration is twice as much as that of something else under the influence of the same causative agent (e.g. the same stretched spring), then we say by definition that the latter is twice as massive as the former.
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