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NooDota
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Homework Statement
I was wondering how do you prove f = m*a, and my teacher said since F = dp/dt and p = m*v then F is m*a
But where did F = dp/dt come from? Does it have a mathematical proof?
NooDota said:Homework Statement
I was wondering how do you prove f = m*a, and my teacher said since F = dp/dt and p = m*v then F is m*a
But where did F = dp/dt come from?
Does it have a mathematical proof?
The equation F = dp/dt, also known as Newton's second law of motion, was first introduced by Sir Isaac Newton in his book "Philosophiæ Naturalis Principia Mathematica" published in 1687.
Newton's second law of motion is a result of his experiments and mathematical calculations on the relationship between force, mass, and acceleration. He observed that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This led to the formulation of the equation F = ma, which was later modified to F = dp/dt to include changes in momentum over time.
Yes, the equation F = dp/dt is applicable to all objects, regardless of their size, shape, or composition. This is because it is a fundamental law of physics that governs the motion of all objects in the universe. However, other factors such as friction and air resistance may affect the motion of objects in real-world situations.
Yes, the equation F = dp/dt is a fundamental law of classical mechanics and is still widely used in modern physics. It is a key component of Newton's three laws of motion and is also fundamental to the study of motion in fields such as astrophysics, fluid dynamics, and quantum mechanics.
While the equation F = dp/dt accurately describes the relationship between force, mass, and acceleration, it does have limitations. It assumes that the mass of an object remains constant, which is not always the case in situations involving nuclear reactions or relativistic speeds. In these cases, more advanced equations such as the relativistic version of Newton's second law or the equations of Einstein's theory of general relativity must be used.