Momentum update with air resistance

[ohheytai]

this isn't really a homework question but yaa its just a question.
how do you integrate the air resistance formula into the momentum update formula??F
Fair = C*$$\rho$$A*v^2
and the momentum update formula is Pfinal=Pinitial +Fg$$\Delta$$t

i used Fg instead of Fnet because in my situation i have falling ball

someone help please :)

 

[fzero]

You can write Newton's 2nd law as

$$\frac{d\vec{p}}{dt} = \vec{F}_g + \vec{F}_{\text{air}},$$

where $$\vec{p} = m \vec{v}$$ is the momentum of the particle.

 

[ohheytai]

yaa i figured it out thanks anywayssss :) do you know how to find change in thermal energy?? like is there an equation?

 

[fzero]

do you know how to find change in thermal energy?? like is there an equation?

It would help to have more details about the system and type of change you're talking about. If you have a specific type of problem in mind, you might want to start a new thread about it.

 

[ohheytai]

its just throwing a ball in the air like what's the change in thermal energy?

 

[fzero]

The energy lost to air resistance is the change in thermal energy. There's a couple of ways to determine it, depending on what information you're given. The energy of the ball is

$$E = \frac{mv^2}{2} + mgh,$$

where $$v$$ is the speed and $$h$$ is the height. If you know the speed is $$v_1$$ at height $$h_1$$ and $$v_2$$ at height $$h_2$$, you can just compute the difference in energies.

There are also some differential equations that you can obtain by considering the work done by air resistance.