A while back if you had received an e-mail from my @hotmail.com account, you would have seen my signature line:
"I wonder at what velosity Bob was shot into the web at? I wonder how much force MB had to exert on that pod to act against the force of gravity to get it to lift off? ... I wonder if I'm spending to much time in physics class?"
Well, sadly...I have answers for all three of those questions.
But, first! Let's get some things under our belt, shall we? (and my applogies to the people in the states. My equations are only in metric format and I'm too lazy to convert them. You can if you want but that's up to you.)
~ = vector symbol
# = total
^ = to the power of
N = Newton
v = velocity (meters per second)
d = distance (meters)
m = mass
t = time (seconds)
a = acceleration
g = gravity
Fg = force of gravity
F(net) = the force that is the opposite of gravity.
It's the force that an object beneath another object to keep it up. (Confused?)
Here are some universal constant factors (I'm using the constants of earth and such 'cause trying to calculate it inside the computer would just be plain impossible!):
~g = 9.8 m/s^2
Mass of Mainframe: 5.98*10^24 kg
G = 6.67*10^-11
Alright, for the first question: I wonder at what velosity Bob was shot into the web at? Let's suppose that - the pod's weight is 500 kilograms; that the distance from the hardware is approx. 400 meters from the web portal; that it takes 5 seconds for Bob to reach the portal (it actually took him 6.3 seconds to reach the portal but that's beside the point! It'll mess up my calculations!); and Bob weights a fairly light 73 kilograms.
Let's have our givens:
pod = 500kg
Bob = 73kg
#d = 400m
#t = 5.0s
What do we need? Velocity! :)
~v = #d/ #t
~v = 400m / 5.0s
~v = 80m/s
So, Bob is shooting towards the portal at a fast 80m/s with transfers to 288 km/h. (Wow. Dat's fast!)
~a = ~v / #t
~a = 80m/s / 5.0 s
~a = 16 m/s^2
But what about gravity?
~a = m*~g
~a = 573kg * 9.8Nkg/m^2 [down]
~a = 5615.4 N/m^2
So, the pod is slowing down 5615.4 N/m^2. What is the force of gravity creating this decelleration?
~Fg = Gmm / #d^2
~Fg = (6.67*10^-11)(573kg)(5.98*10^24 kg) / (400m)^2
~Fg = 1.43*10^12 N
Next question: I wonder how much force MB had to exert on that pod to act against the force of gravity to get it to lift off?
F(n) = m * ~a
F(n) = 573kg / 16/m^2
F(n) = 9168 N
Third and final question: ... I wonder if I'm spending to much time in physics class? I think it's safe to say...Yes! Yes I have. WAY too much time in phyics class and getting too bored at that! So...that's it! That's how fast Bob was shot into the Web...My next assignment for myself? Find out how fast game cubes fall. *g*
And who said that physics wasn't fun?