Derivation of Newton's F = ma: Help Needed

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In summary, Newton's law states that force is proportional to the acceleration experienced by an object.
  • #36
Bhargava2011 said:
No, I'm not at all going outside of simple Classical Mechanics.

That depends on the type of systems your statement ("its not at all necessary to have a linear relation between m*a and force") was related to. For open systems you are right but for closed systems you already are outside classical mechanics.

Bhargava2011 said:
When going by Newton's second law we'll get a relationship between F and m*A of the form F=K*m*A (where k is a constant).

For closed systems this is basically correct but in addition to Newtons second law you also need the third law, definition II, Galilei transformation, isotropy and maybe even more.
 
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  • #37
epenguin said:
Not read all thread so this may have been said. The point is often fudged in teaching.
[..] You can measure a, but you cannot in the first place measure F and m independently. So this is not an empirical law, more of a definition. [..]

As mentioned before: The equality sign F=ma is a later simplification (k=1) that came with the introduction of standard unit systems; it is due to a free choice of units.

For deriving F~ma Newton could compare identical "impressed forces" by observing an equal amount of impression of a spring, and he could also compare identical "masses" by means of equilibrium of a balance. Neither Newton nor Hooke were completely free to define "Force" as they liked.
 
<h2>1. What is Newton's second law of motion?</h2><p>Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. In other words, the greater the force applied to an object, the greater its acceleration will be, and the more massive an object is, the less it will accelerate under the same force.</p><h2>2. How is Newton's second law mathematically represented?</h2><p>Newton's second law is mathematically represented as F = ma, where F represents the net force applied to an object, m represents the mass of the object, and a represents the resulting acceleration of the object.</p><h2>3. What is the derivation of Newton's second law?</h2><p>The derivation of Newton's second law involves using calculus to analyze the motion of an object under the influence of a constant net force. By applying the principles of calculus, we can show that the resulting acceleration of the object is directly proportional to the net force and inversely proportional to its mass, leading to the equation F = ma.</p><h2>4. Why is Newton's second law important?</h2><p>Newton's second law is important because it is one of the fundamental principles of physics that helps us understand and predict the motion of objects. It is also the basis for many other laws and equations in physics, and it has numerous practical applications in fields such as engineering, mechanics, and astronomy.</p><h2>5. Can Newton's second law be applied to all types of motion?</h2><p>Yes, Newton's second law can be applied to all types of motion, whether it is linear, circular, or rotational. As long as there is a net force acting on an object, its acceleration can be determined using the equation F = ma.</p>

1. What is Newton's second law of motion?

Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. In other words, the greater the force applied to an object, the greater its acceleration will be, and the more massive an object is, the less it will accelerate under the same force.

2. How is Newton's second law mathematically represented?

Newton's second law is mathematically represented as F = ma, where F represents the net force applied to an object, m represents the mass of the object, and a represents the resulting acceleration of the object.

3. What is the derivation of Newton's second law?

The derivation of Newton's second law involves using calculus to analyze the motion of an object under the influence of a constant net force. By applying the principles of calculus, we can show that the resulting acceleration of the object is directly proportional to the net force and inversely proportional to its mass, leading to the equation F = ma.

4. Why is Newton's second law important?

Newton's second law is important because it is one of the fundamental principles of physics that helps us understand and predict the motion of objects. It is also the basis for many other laws and equations in physics, and it has numerous practical applications in fields such as engineering, mechanics, and astronomy.

5. Can Newton's second law be applied to all types of motion?

Yes, Newton's second law can be applied to all types of motion, whether it is linear, circular, or rotational. As long as there is a net force acting on an object, its acceleration can be determined using the equation F = ma.

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