Modeling with Differential Equations

[aaronfue]

Homework Statement

A falling body of mass m, encounters air resistance proportional to its instantaneous velocity, v. Use Newton's second law to find the DE for the velocity, v at time, t.

Homework Equations

I've been reading this section quite a bit and am still not getting it! I'd appreciate a simple breakdown of this problem.

The Attempt at a Solution

I know Newton's second law is F=ma, and a=[itex]\frac{dv}{dt}[/itex]= -g, in this problem. I've checked the answer in the back of the book to see if I can work it backwards and then maybe get an idea of what's going on, but I don't think I've dealt with air resistance, k, in any problems before. Even in my physics class.

 

[SammyS]

Homework Statement

A falling body of mass m, encounters air resistance proportional to its instantaneous velocity, v. Use Newton's second law to find the DE for the velocity, v at time, t.

Homework Equations

I've been reading this section quite a bit and am still not getting it! I'd appreciate a simple breakdown of this problem.

The Attempt at a Solution

I know Newton's second law is F=ma, and a=[itex]\frac{dv}{dt}[/itex]= -g, in this problem. I've checked the answer in the back of the book to see if I can work it backwards and then maybe get an idea of what's going on, but I don't think I've dealt with air resistance, k, in any problems before. Even in my physics class.

Newton's 2nd Law: The net force on a body of mass, m, is given by F_net = ma .

For this problem F_net = mg - kv , and is in the downward direction.

 

[aaronfue]

Newton's 2nd Law: The net force on a body of mass, m, is given by F_net = ma .

For this problem F_net = mg - kv , and is in the downward direction.

I see. There was an image next to the question with those being opposite. Now to put ity into a differential equation form? I was watching a video about differential equations and there being a 1st ODE format using p(x) and q(x)?

 

[haruspex]

Now to put it into a differential equation form?

What differential equation relates acceleration to velocity?