- #1
sedaw
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F = dp/dt = d(mv)/dt = m(dv/dt) + v(dm/dt) = a + v(dm/dt)
i don't understand why d(mv)/dt = m(dv/dt) + v(dm/dt)
can somone help ?
TNX !
i don't understand why d(mv)/dt = m(dv/dt) + v(dm/dt)
can somone help ?
TNX !
irycio said:Well, written in the form of
[tex] F=m \frac{dv}{dt} [/tex]
it is valid inly for constant mass system since you assume that the mass is constant :P.
But assuming, that mass is dependant on velocity, which is true (according to SR) you get what sedaw wrote.
Thus, the best, most general form of Newton's 2nd law is
[tex] F=\frac{dp}{dt} [/tex]
as it doesn't imply anything being constant ;P
Newton's 2nd Law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
In variable mass systems, the mass of the object is not constant and can change over time. Newton's 2nd Law can still be applied in these cases by considering the change in mass and using the concept of the "center of mass."
One example of a variable mass system is a rocket. As the rocket burns fuel and expels it, the mass of the rocket changes and thus affects its acceleration according to Newton's 2nd Law.
The generalization of Newton's 2nd Law for variable mass systems is known as the "rocket equation," which takes into account the change in mass and the exhaust velocity of the expelled mass to calculate the acceleration of the system.
The generalization of Newton's 2nd Law is crucial in space travel as it allows for the calculation of the necessary fuel and thrust needed to reach a desired destination. It also helps in the design and operation of spacecraft, taking into account the changing mass and acceleration of the system.