Newton's second law for mass changing

Описание: Welcome back to my make me curious.
This video is about newton second law for mass changing case.



Today we're going to talk about Newton's second law, but with a twist. Imagine a situation in which the body is moving very fast, so according to Einstein the mass of the object increases then how do we use newton’s second law to calculate the amount of force acting on that body? In that case, we have to modify our equation F = ma a bit. As you remember from the last video, newton’s second law actually says that the force acting on a body is equal to the change in momentum divided by time. We know that p momentum is equal to the product of mass and velocity. Now that mass is changing, we have to do some modifications to calculate the force on the body.
Let’s go to the derivation of the equation for mass changing.
Now apply the product rule of differentiation on change in mass and velocity divided by the change in time.
So the force is then equal to mass multiplied by the change in velocity divided by the change in time. Plus velocity multiplies the change in mass divided by the change in time. Now, this is the equation that can be used to know the force applied on the object whose mass is changing.
Now if the mass is constant then the change in mass will become zero and then the whole term will become zero because when you multiply zero with something it gives you a zero result, now change in velocity divided by the change in time is called acceleration and that is how you go back to Newton’s second law common equation F = ma
And that's it for today. Thank you for watching and I hope you learned something new about Newton's second law for changing the mass of an object.

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