Mechanics Clarification (1 Viewer)

[Casper_18]

I am having a bit of trouble

For examble a particle is moving downards with a resistance proportional to v²

In this part you get an equation that looks like:

ma = mg - mkv²

What I dont understand is why the resistance is equal to mkv² when there is no mention that it is proportional to the mass aswell.

 

[Drongoski]

I am having a bit of trouble

For examble a particle is moving downards with a resistance proportional to v²

In this part you get an equation that looks like:

ma = mg - mkv²

What I dont understand is why the resistance is equal to mkv² when there is no mention that it is proportional to the mass aswell.

resistance r being proportional to v² means r = Kv². This can be restated if reqd as r = mkv² where the K = mk; e.g. if K = 12 and mass m = 4, then k = 3 - makes little difference.

Stating it in the form: ma = mg - mkv² = m(g - kv² ) enables you to say a = g - kv² as this can sometimes be useful.

 

[Casper_18]

Thanks, that helps me out heaps.

 

[whackymac]

All forces are in the form F = ma.

Since they stated the "acceleration" of the resistance which is kv^2, the Net Force would be:

Fnet = force of gravity - force of resistance
= mg - m.kv^2

Therefore, ma = mg - mkv^2