If we have a mass function of time i.e M(t) then F=(m.v') or F=(m.v)' and why ?

[Arslan]

If we have a mass function of time i.e M(t) then F=(m.v') or F=(m.v)' and why ?

If we have a mass function of time i.e M(t) then F=(m.v') or F=(m.v)' and why ?

 

[ZapperZ]

If we have a mass function of time i.e M(t) then F=(m.v') or F=(m.v)' and why ?

Write down the more general form of the equation, i.e.

F = \frac{dp}{dt}

where p=mv.

Now do the differentiation with respect to time.

Zz.

 

[Arslan]

but why
i have been reading this expression of force F=(m.v') since i was in school and we also read the reasons for the occurrence of this formulie

and now the expression changes to F=(m.v)'

if mass is the function of time these two formulais yields different results. If the second one is the correct one , then i need explanations why?

 

[Brin]

Think about it, we have (because of the product rule),
F=\frac{dp}{dt}=\frac{d}{dt}\left(mv\right)=m\frac{dv}{dt}+\frac{dm}{dt}v
Normally, when we “Talk Newtonian” the mass is consant, so, \frac{dm}{dt}=0 and thus, F=m\frac{dv}{dt}

Likewise, there might be situations where \frac{dv}{dt}=0 and so F=\frac{dm}{dt}v

 

[ZapperZ]

but why
i have been reading this expression of force F=(m.v') since i was in school and we also read the reasons for the occurrence of this formulie

and now the expression changes to F=(m.v)'

if mass is the function of time these two formulais yields different results. If the second one is the correct one , then i need explanations why?

I don't understand what you are having a problem with here. Are you asking for examples for when mass isn't a constant over time? Or you just don't understand how to derive such an expression? You never indicated that you had done what I told you to do, i.e. taking the derivative. If you did, you would have clearly seen that you get two terms, one being the beloved "ma", the other having the time derivative of the mass.

So what is it here that you are objecting to that needs explanation?

Zz.

 

[Arslan]

Think about it, we have (because of the product rule),
F=\frac{dp}{dt}=\frac{d}{dt}\left(mv\right)=m\frac{dv}{dt}+\frac{dm}{dt}v
Normally, when we “Talk Newtonian” the mass is consant, so, \frac{dm}{dt}=0 and thus, F=m\frac{dv}{dt}

Likewise, there might be situations where \frac{dv}{dt}=0 and so F=\frac{dm}{dt}v

I know the mathematical terminolgies an expansion
i want to know, if M is function of time why we can't use F=mv' because this formulie make sense that if a force is applied on body it will accelrate(i.e. its velocity will chnge) and "m" is the constan of propotionality, if mass is varying the instantanious value of force are correct too if we plug them in F=mv'.

then why, why and why F=(mv)'

 

[sed199]

by definition, force is the change in momentum with respect for time. Momentum is defined as p=mv. If we are to assume m as constant, as it convieniently is in most cases,
f=d(p)/dt=d(mv)/dt=m(dv/dt)=ma

But if M was a function of time and represented as m(t), we are stating that mass may take a value of zero or may be invariant with respect to time dependending on what the fuction
m(t) is. So as we would do in calculus when we are taking the deriviative of two fuctions that are a functions of the independent variable, we use the product rule.
f(t)=m(t)*(dv(t)/dt)+(dm(t)/dt)*v(t)

 

[Rap]

A more intuitive answer - if you push on a bucket of water (constant mass), without friction, it will have a constant acceleration - that's an experimental fact. How hard you push is the force, so F=mv'. But what if you push on it with the same force, while somebody keeps adding water to it? It will not accelerate as much. Someone could pour water in at just the right rate so that as you pushed on it, its velocity stayed the same, no acceleration. It turns out that the rate they have to pour it in is a steady rate, equal to the velocity times that rate in mass/second. In other words, we know by experiment that F=mv' when m is constant and we know by experiment that F=m'v when v is constant. That means F=m'v+v'm = (mv)'.

If you ask why does F=m'v when the velocity is constant, then you can just as easily ask why does F=mv' when m is constant. That would be a more complicated question.

 

[Arslan]

thanks brother that's what i was looking for...once again thanks for giving such a wonderful answer