A question for anyone knowledgeable in physics

[Wooh]

Hello, a good fellow at a forum I frequent led me to the good people of this forum. He said they were up to this. I need a formula, please, if possible, help me out. Basically, I need to know how high a ball is after being applied a variable amount of force, in a variable amount of gravity. If you need to know how long the force is applied, then that is variable too. The mass of the object, too, is variable. And, if possible, please tell me how to imput all the data (What format, joules etc). Thank you for your time.

[Ender]

Dammit Wooh, you could have been a bit more diplomatic then that.

[Wooh]

Sorry for my lack of tact and diplomacy, I am used to very casual forums

[SWPIGWANG]

k.e=p.e=m*g*h=F*d

g is gravitation field strengh, find it by using GM/R^2 , M being the source of gravity (usually the planet)

m is the mass of the object

F is the force net

d is the net distance the force is applied

convert it from time using d = (1/2)*(F/m)*t^2

h is the height, or your result.


This formula should work for short distances (no big change in g) and low speeds where other factors can be ignored (friction and relativitic crap..etc)

[SWPIGWANG]

Just solve the equation than use dimensional analysis to find the units.

[XaLEv]

Sorry for my lack of tact and diplomacy, I am used to very casual forums

I think he was being sarcastic. Can't be sure till he says more.

[Wooh]

Sarcasm? NEVER! and thank you very much, SWPIGWANG

[Darth Wong]

If everything is continuously variable, then you're looking at calculus, and probably a numerical solution rather than an analytical solution.

[Crown]

Change that probably to a definetly.

Wooh, I have the sinking suspiscion that you are after Tsiolkovsky's Rocket Equation, variable mass, variable gravity and variable force? Yep sounds like the usual suspect.

Or are you looking for a generic equation to determine the heigt of the ball, and then use some kind of spreadsheet or program like MATLAB to see the different heights when the variables are varried? Sorry I am just seeking a little crarity that's all.

[SWPIGWANG]

varible as in changing over time?

ah I hate integration....

[Wooh]

Change that probably to a definetly.

Wooh, I have the sinking suspiscion that you are after Tsiolkovsky's Rocket Equation, variable mass, variable gravity and variable force? Yep sounds like the usual suspect.

Or are you looking for a generic equation to determine the heigt of the ball, and then use some kind of spreadsheet or program like MATLAB to see the different heights when the variables are varried? Sorry I am just seeking a little crarity that's all.

The second one, except I want to use it in a program, where if have the time and the 4 variables (mass, gravity, force, and time that force is applied), i can get the height at say, 1 second, 2 second, etc. Nothing quite as complex as the rocket formula, because none of the variables change.

[Crown]

In that case;

v^2 = u^2 + 2as

a = accleration and is negative.

u = initial velocity

v = final velocit

At greatest height, final velocity is equal to 0.

The initial velocity is a little tricky, but can be found as follows;

F = ma
F = m*(u/t)

therefor u = t*(F/m)

You could assume that the Force is applied instanteousley, t = 1, and then you can get u very easily.

Which gives you a greatest height of;

s = (-u^2)/2a

To see the different heights you could use Excel, by setting up a data table (see Excel's help page) but this will limit you to only being able to vary two of the variables.

[Crown]

I think that's right, and I hope that that's what you were after.

[Wooh]

thank you very much, I will experiment with that and my program, hopefully it will work

[Durandal]

Hello, a good fellow at a forum I frequent led me to the good people of this forum. He said they were up to this. I need a formula, please, if possible, help me out. Basically, I need to know how high a ball is after being applied a variable amount of force, in a variable amount of gravity. If you need to know how long the force is applied, then that is variable too. The mass of the object, too, is variable. And, if possible, please tell me how to imput all the data (What format, joules etc). Thank you for your time.

Wow ... this sounds like a complex problem. If mass, force and gravity are variable, you'll probably be looking at a triple integral. Your output unit will obviously be meters, since you're looking for height.

Could you give us the exact problem? This is difficult to do analytically. Is the ball being launched straight up? What is the initial velocity? What is the launching angle?

Since gravitational acceleration is variable, you'll probably be looking at the equation

F = GMm/r^2

as your base equation.

[Wicked Pilot]

It's kinda hard to understand what you're asking for here. Can you provide a problem, or a sample problem we could use to understand what you're looking for?

[Wooh]

Hello, a good fellow at a forum I frequent led me to the good people of this forum. He said they were up to this. I need a formula, please, if possible, help me out. Basically, I need to know how high a ball is after being applied a variable amount of force, in a variable amount of gravity. If you need to know how long the force is applied, then that is variable too. The mass of the object, too, is variable. And, if possible, please tell me how to imput all the data (What format, joules etc). Thank you for your time.

Wow ... this sounds like a complex problem. If mass, force and gravity are variable, you'll probably be looking at a triple integral. Your output unit will obviously be meters, since you're looking for height.

Could you give us the exact problem? This is difficult to do analytically. Is the ball being launched straight up? What is the initial velocity? What is the launching angle?

Since gravitational acceleration is variable, you'll probably be looking at the equation

F = GMm/r^2

as your base equation.

I want to keep them variable, it is going to get user imput and then figure out the height.

[Wooh]

An example: You have a ball, resting on a platform. The ball weighs 2 grams. The gravity of the area the ball is in is 3x the normal earth gravity. For 5 seconds, 10 newtons of net force is added - this is the force over the amount needed to break free of the gravitational pull so the ball doesn't just sit on the platform. Find when the ball peaks, at how high, when the ball hits the ground, and say...the height of the ball at 2 seconds, 5 seconds, 7 second, 9 seconds, any amount of seconds, really.

[Wicked Pilot]

An example: You have a ball, resting on a platform. The ball weighs 2 grams. The gravity of the area the ball is in is 3x the normal earth gravity. For 5 seconds, 10 newtons of net force is added - this is the force over the amount needed to break free of the gravitational pull so the ball doesn't just sit on the platform. Find when the ball peaks, at how high, when the ball hits the ground, and say...the height of the ball at 2 seconds, 5 seconds, 7 second, 9 seconds, any amount of seconds, really.

Alright, first we find the initial velocity of the ball at release. For this we will use the equation:

vi=at, a=F/m, vi=Fi/m
(i=impulse time)
(vi=initial velocity)
(F=force)
(m=mass)


now we will need to know how long it will take for the ball to reach a final, zero velocity. We get this by the equation:

vf=vi-gt, t=(vi-vf)/g
(vf=final velocity)
(g=acceleration due to gravity)
(t=time)

now we fing the height using the equation:

h=.5gt^2
(h=height ball will achieve)

therefore, if we add together all the equations, we get the mother equation of:

h=.5g(((fi/m)=vf)/g)^2


I hope this helps. Somebody please be so kind as to check my work, I'm not perfect.

[Wooh]

h=.5g(((fi/m)=vf)/g)^2
What symbol should the = sign be?

[Wicked Pilot]

h=.5g(((fi/m)-vf)/g)^2



sorry, as I said, sombody should check my work

[Wooh]

Hmm, if there is no t in that equation, how can one find the height of the ball at a given point in time?

[data_link]

h=.5g(((fi/m)-vf)/g)^2



sorry, as I said, sombody should check my work

vf is an unnessecary term because vf=0.

Also, using i is confusing. It is better to use t.

You can simplify this equation further by canceling the g.

Therefore, h=(.5(Ft/m)^2)/g

Where h is the maximum height of the ball, F is the force applied at launch (above the force of gravity), t is the time for which said force is applied, and g is the acceleration due to gravity.

[Wooh]

h=.5g(((fi/m)-vf)/g)^2



sorry, as I said, sombody should check my work

vf is an unnessecary term because vf=0.

Also, using i is confusing. It is better to use t.

You can simplify this equation further by canceling the g.

Therefore, h=(.5(Ft/m)^2)/g

Where h is the maximum height of the ball, F is the force applied at launch (above the force of gravity), t is the time for which said force is applied, and g is the acceleration due to gravity.

is h only the maximum height (peak), or the height at the given value for t?

[data_link]

h is the maximun height. t is the time for which the force is applied.

If you want to find the height at one particular moment in time, then you would use h = vi - .5gt^2, where h is height, vi is the initial velocity of the ball, g is the acceleration due to gravity, and t is the time after launch.