Newton's Second Law

[KindofSlow]

Hello,
I am just starting differential equations.
On this page: http://tutorial.math.lamar.edu/Classes/DE/Definitions.aspx
the Professor writes F=ma, a = dv/dt, m dv/dt = F(t,v).
I understand the first two equations. My question is on the third equation, what happened to the m?
Mass seems to disappear from the left side of the equation to the right side.
I've hypothesized that maybe v is a function of m so m is hidden in v on the right side but I don't even know if that makes sense.
Any illumination will be appreciated.
Thank you

 

[akoaysigod]

F(t, v) is a function of time and velocity, which in this case, is force. Saying ma=F is equivalent to m dv/dt = F(t,v), if the context is correct. If you had mass on both sides you'd have acceleration, in this example, equals a function of time and velocity, which could be correct but it wouldn't be force. I hope that makes sense. The notation can be confusing at times but you'll get used it. I hope that made sense.

 

[KindofSlow]

Thank you

 

[wjm11]

the Professor writes F=ma, a = dv/dt, m dv/dt = F(t,v).
I understand the first two equations. My question is on the third equation, what happened to the m?
Mass seems to disappear from the left side of the equation to the right side.

Acceleration depends on both velocity and time: a = dv/dt

Force equals mass times acceleration: F = ma

A simple substitution yields: F = m(dv/dt)

This is a practical/useful form of the equation since in many physics problems, m remains constant, but velocity is often changing with time.

(This is not true for a chemical rocket or missile, where fuel (mass) is being consumed and therefore changing with time.)

Hope that helps.