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IWantToLearn
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I wonder why Newton second law, define force as mass x acceleration, acceleration is the second time derivative of displacement, why he didn't define the force as mass x higher order time derivatives of displacement
A technical, but important point to note is that force is not defined as mass times acceleration, but instead as:IWantToLearn said:I wonder why Newton second law, define force as mass x acceleration, acceleration is the second time derivative of displacement, why he didn't define the force as mass x higher order time derivatives of displacement
Albertrichardf said:Also, if you are not convinced about the fact that we choose the definitions, look at relativity. Momentum was redefined to preserve covariance of the law and its conservation. The force was not redefined, nor was the work done, so you really do get to choose what you want.
It depends on how you see it I guess. I look at the force as being defined by its relation to momentum, so I don't see it as being redefined. But if you were to compute the derivative you do end up with a different equation for the force. In a sense that is a redefinition.PeroK said:It seems to me that you could equally argue that if you redefine momentum and keep the same relationship between momentum and force, then you have redefined force.
Albertrichardf said:Momentum was redefined to preserve covariance of the law and its conservation.
Albertrichardf said:I was under the impression that momentum was also redefined as ##\gamma m_ov##.
Albertrichardf said:According to this paper, momentum is the one that's redefined: http://www.phys.ufl.edu/~acosta/phy2061/lectures/Relativity4.pdf.
Albertrichardf said:I"We need a new definition of momentum to retain the definition of force as a change in momentum", and that "In this definition of momentum, the mass m=m0 is the “rest mass”"
WelcomeIWantToLearn said:Thanks :)
DrStupid said:In my calculation (see link above) I demonstrated how the relativistic momentum results from the original definitions if Galilean transformation is replaced by Lorentz transformation - without any redefinitions. The old definition is just rewritten using a new concept of mass. And even the new concept of mass is not a requirement in relativity. Relativistic mass would do the job as well. Using rest mass instead is just more comfortable.
Albertrichardf said:It is possible to keep the old definition of momentum, but you can also redefine the momentum instead, as the paper as shown.
Albertrichardf said:There was a paper that used a Hamiltonian equation of motion (the derivative of the Hamiltonian with respect to the momentum is the velocity.) plus the fact that for kinetic energy to be conserved in two frames, the momentum must be conserved as well.
DrStupid said:That sounds much better. In this case momentum is not defined by an equation but by its's porperties. This is indeed another definition even though it is desigend to be in line with the original definition.
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 simpler terms, 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.
Revisiting Newton's Second Law allows us to better understand the relationship between force, mass, and acceleration and how they affect the motion of objects. It also allows us to apply this law to various real-life situations and make accurate predictions about the behavior of objects.
Newton's Second Law is closely related to the other two laws of motion. The first law, also known as the Law of Inertia, states that an object will remain at rest or in motion at a constant speed unless acted upon by an external force. This can be seen as a special case of Newton's Second Law, where the net force acting on the object is zero. The third law, or the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction. This law can be applied to situations where the net force is not zero.
Yes, Newton's Second Law can be applied to both inertial and non-inertial reference frames. In an inertial reference frame, the net force on an object equals its mass multiplied by its acceleration. In a non-inertial reference frame, the net force also includes any fictitious forces that may be present due to the acceleration of the frame itself.
To calculate the force on an object using Newton's Second Law, we can use the formula F = ma, where F is the net force, m is the mass of the object, and a is the acceleration. This can be used to determine the force needed to accelerate an object to a certain speed or to calculate the acceleration of an object under a given force.