Just a question on terminal velocity

[flyingpig]

Homework Statement

It is a definition that the terminal velocity is the same as constant velocity where the net force is 0 and therefore the acceleration is also 0

Here is what I don't get, why must the terminal velocity must such that it is constant? I know that to be "terminal" it means it can no longer change it's velocity, but how come gravity will able to counteract it such that the sum of forces is 0? I mean what if air resistance is so strong that gravity can't counteract it? Wouldn't it mean the sum of forces is no longer 0 and the terminal velocity can never be reached or at that point, that is the terminal velocity?

 

[tiny-tim]

hi flyingpig!

… what if air resistance is so strong that gravity can't counteract it? Wouldn't it mean the sum of forces is no longer 0 and the terminal velocity can never be reached or at that point, that is the terminal velocity?

air resistance depends on speed …

if air resistance is very strong, that means that it is very much stronger than usual for each particular speed …

so air resistance will balance gravity at a lower speed …

ie terminal velocity is lower

(oh, and terminal velocity is never quite reached anyway … the speed gets exponentially close to terminal velocity )

 

[flyingpig]

hi flyingpig!


air resistance depends on speed …

if air resistance is very strong, that means that it is very much stronger than usual for each particular speed …

so air resistance will balance gravity at a lower speed …

ie terminal velocity is lower

(oh, and terminal velocity is never quite reached anyway … the speed gets exponentially close to terminal velocity )

That is even more confusing now...

I just don't understand why or how gravity can balance out the terminal speed.

 

[tiny-tim]

when v = 0, air resistance (let's call it R(v)) is 0,

so using a = F/m, we have a = mg/m = g

when R(v) is larger, a = (g - R(v))/m < g;

eventually R(v) = g, and then a = 0, ie the speed is constant