Physics/calculus/programming problem

[Burner]

Ok, so i'm working on this problem:

A referee throws a jump ball vertically in the air. Besides the force
of gravity, the drag force acts on the ball. The drag force is given by
the product of the friction coefficient with the square of the velocity.
The friction coefficient is 0.1. The NBA ball mass is 0.6 kilograms. The
initial ball velocity is 10 meters/second. How much time does it take
for the ball to slow down to 2 meters/second?

So what I'm doing:

force balance:
Ma = Mg + Fd

where: Fd= kV^2
k/m=0.167
So:

x_double_dot = 9.8 + 0.167(x_dot)^2


Its been a while since i have done any programming, but i'm trying to use the ode45 command in matlab to solve it, however i'm doing something wrong, take a look:

(yprime.m first m file )
function dy = yprime(t,y)
dy = [y(2); 0.167 * y(2)^2 + 9.8];


(odedem.m this m file calls the yprime m file)
[t,Y] = ode45(@yprime, [0 10], [0 10])

plot(t,Y);

So right now i have t going from 0-10 and the initial condictions y(0)=0 and y'(0)=10

Can anyone at least point me in some direction (different method?), kinda stumped at the moment.

 

[sogone2day]

E=mc^2 W=fd Thats All I Got.

 

[jmh80]

Oh, dear God.
I hated Matlab more than anything in my entire life during frosh engineering.

Lemme think about this. I'll have to draw it out.
I've been out of ChE undergrad for almost 2 years - been 4 since physics.

 

[jmh80]

I take the year back when I took regular physics. It was 1999 when I took this ****.
I don't have any of my stuff from that class.
I could really help you design a heat exchanger or anything with distillation.

I went to this site for some eqns:
http://www.collegeboard.com/prod_downloads/ap/students/physics/info_equation_tables_2002.pdf

Looks like you need the following:
F(net) = m*a

v = v(0) + a*t

where F(net) = F(gravity) - F(drag)
I think that is part of a problem with your overall force balance. Gravity's vector is down but drag would be upward.
Here: drag acts opposite the direction of motion of an airplane.
http://www.grc.nasa.gov/WWW/K-12/airplane/drag1.html

So, F(net) = m*g - f*v^2

Solving for t, t = (v-v(0))/((m*g-f*v^2)/m)

My question for myself is what velocity do you use to calculate the drag force? The velocity changes at every point.

 

[jmh80]

Wait, now that I think about it. I assume this problem calls for the ball to be thrown upward and that it doesn't begin to fall downward.

So, then your force balance would be mg+fv^2 since drag and gravity would be both acting downward due to the ball going upward during it's flight.

 

[Burner]

Right, as the ball is going up it's experiencing gravity and drag (Mg+Fd) slowing it down. Its inertial force is pointing up (Ma, where a=the balls acceleration which is negative as it’s going up). The drag force is constantly changing with the balls velocity, that’s partly what makes this problem difficult and I'm also pretty sure you cant use the kinematic equations. I’m pretty sure my original equation is correct as it takes into account the drag with respect to velocity (or time), but i could be wrong. Anyone have maple and know how to use it?

 

[jmh80]

I don't understand your equation.
You seem to have forgotten the mass in the force due to gravity term.

I suppose drag force is a differential term.

 

[Burner]

Well i didnt write out all the steps, i devided the entire question by M...

Ma = Mg + Fd --> a = g + Fd/m --> x_dbl_dot= g + c/m*(x_dot)^2

Drag force = Fd = cV^2

And we have: M=0.6Kg
friction coeff. c=0.1
0.1/0.6~0.167

So final eq: x_dbl_dot= 9.8 + 0.167*(x_dot)^2

Its time dependant so i wrote it as x_dbl_dot and x_dot, however, a cleaner but not as accurate way to write it would be x''= 9.8 + 0.167(x')^2

 

[jmh80]

Ahh.
Well, I'm tapped out on this and it's late.
Good luck.