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We’ll fix it right now! Here is this system, in this form: The total momentum is LINK DELETED AGAIN This suggests that “external forces” act on this system in this form! If you release the system from external influences, then the LINK DELETED AGAIN of this system will look like this: Did you define it "by eye"?

Velocity for one.  No! For one material object of constant mass: [math]\frac{{d\vec p}}{{dt}} = \frac{{d(m\vec v)}}{{dt}} = m\frac{{d\vec v}}{{dt}} = m\vec a[/math] For one material object of variable mass: [math]\frac{{d\vec p}}{{dt}} = \frac{{d(m\vec v)}}{{dt}} = m\frac{{d\vec v}}{{dt}} + {v_r}\frac{{dm}}{{dt}} = m\vec a + {{\vec F}^j}[/math] momentum - is NOT velocity change in momentum - is NOT a change in velocity the immutability of the momentum - is NOT the immutability of velocity!

Is that bad? Lets, remember Physics! Its basic concepts! What do "external forces" change? What can not change the system of material bodies without "external force"?

The total momentum of this system is Zero. It is no more and no less than zero - it is strictly equal to Zero! [math]{p_{var}}(t) = {m_{liquid}}(t){\vec v_1}(t) + {m_{case}}(t){\vec v_2}(t) = 0[/math] There is no other solution! There is no other law of conservation of momentum! A VARIPEND is any centrifugal pump operating in the mode of periodically breaking the flow of a pumped substance. What “such things” are not possible under conservation laws? If you see the Center of Mass of this pretty mechanical system and you see it clearly, then this CM violates the "conservation laws" that are obvious to you, then you need to contact your psychotherapist immediately - he will help you cure not only your eyesight!

Let me introduce for your attention a very interesting mechanical system. It is called: "Varipend." Variable pendulum ( VariPend = VARIable + PENDulum) A pendulum of variable length and mass, implemented in an isolated system. - the case increases its mass - working moving mass decreases The mass of the entire system is unchanged! [math]M(t) = {m_{liquid}}(t) + {m_{case}}(t) = const[/math] The total momentum of the Varipend system: [math]{{\vec p}_{var}}(t) = {m_{liquid}}(t)\;{{\vec v}_1}(t) + {m_{case}}(t)\;{{\vec v}_2}(t)[/math] In Mechanics, there is a Law of Conservation of Momentum (LCM): Which states that the TOTAL MOMENTUM of the mechanical system - without external forces - IS STABLE. Here is this system, in this form: The total momentum is LINK DELETED ! This suggests that “external forces” act on this system in this form! If you release the system from external influences, then the LINK DELETED of this system will look like this: This is a simple solution to a LINK DELETED! [math]{p_{var}}(t) = {m_{liquid}}(t){{\vec v}_1}(t) + {m_{case}}(t){{\vec v}_2}(t) = 0[/math] You can explore the same mechanical system by solving the LINK DELETED This solution is using a mechanical Lagrangian : =============================== Before you is the law of conservation of momentum and the law of conservation of energy! In pure form! =============================== This task is not mathematically complicated. But she is very, very difficult in terms of psychology ....