How do you compute the force to apply to a mass to move it some distance in a given amount of time?

Specifically, say you've got a mass of value X and you want to move it Y units in Z time. We can assume the classic simplistic spherical shape, vacuum, and no friction.

(I'm embarassed to ask this -- I could have solved this when I was 15, but I haven't done any physics since highschool -- and I guess at 31 I'm an old man now )

Assuming you're applying a constant force, you have

F/m = a = d^2x/dt

so that (assuming zero initial velocity and position)

x = at^2/2 = Ft^2/2m

Thus

F = 2mx/t^2

Hope this helps.

That does look like it will help -- I appreciate it. Now, I realize, that it will be important to be able to apply this to moving masses as well to correct their position. Is there a formalization of that?

EDIT: I figure this is extrapolatable by taking the difference in position of where the mass would be if left alone from where I want it to be, and then apply forces accordingly.

If you have a non-zero initial velocity (i.e. moving mass) you would have an extra term

x=at^2/2 + vt

so

F=ma=2m(x-vt)/t^2

These don't give you any guarantees on how fast it will be when it gets there. Anyway, could you explain the nature of your position correction in a little more detail? (i.e. Do you want to take a moving object and stop it at a given position? Do you want to correct its trajectory so that it passes through a given point? What constraints do you need for the velocity when it gets there?)

Nevada Wrote:If you have a non-zero initial velocity (i.e. moving mass) you would have an extra term

x=at^2/2 + vt

so

F=ma=2m(x-vt)/t^2

These don't give you any guarantees on how fast it will be when it gets there. Anyway, could you explain the nature of your position correction in a little more detail? (i.e. Do you want to take a moving object and stop it at a given position? Do you want to correct its trajectory so that it passes through a given point? What constraints do you need for the velocity when it gets there?)

Thanks, nevada!

I have two intended usages for this.

1) I want to implement a more correct controller for "servos" in my simulation environment. I use ODE to model physics ( though I'm experimenting with Bullet right now) -- but since ODE's pretty general purpose doing things like making a servo or linear actuator move to a particular point can require direct setting of forces. My current implementation works reasonably well, but is a little primitive.

2) I've implemented a "gravity gun" like function for mouse picking, allowing movement of objects in the scene by clicking and dragging. It works, but it's primitive. I'm interested in a smarter algorithm, and as I said in the beginning, I could have done this 15 years ago. Since then I've studied a lot of things, but not physics. I remember stuff like F = m*a but that's about it....

Hey, Nevada

I want to thank you -- it works beautifully.

Glad I can help. I especially enjoy helping with things like this.