elrnd said:
I am wanting to use an electomagnet to repell an object of about 8.42 GRAMs for a distance of approximately 100 yards. It will be traveling roughly horizontal to the ground, starting at approximately 1.3 meters above the ground, so:
I am trying to figure out how much force I need to create to propell the object (lets assume a sphere for the moment to keep air resistance simple) 100 yard before it drops more than 10cm.
OK, now we have a specific scenario to talk about. So this is sort of an electromagnetic gun, right? I assume the "barrel" of the gun is relatively short, so that for most of its flight, the object is an ordinary projectile, subject only to gravity and air resistance.
In that case, you've got basically a two-stage problem: (1) find out how fast the object needs to be moving when it leaves the gun, so that it will drop 10cm after traveling 100m horizontally; (2) find out how much force the gun needs to exert on the object while it's inside the gun, given information like the length of the gun's "barrel" and how much friction acts on the object while it's traveling through the gun.
If you didn't have to worry about air resistance, step (1) would be a fairly simple exercise in two-dimensional projectile motion. But for an 8.42-gram object traveling 100m, air resistance is going to be
very significant. The force of air resistance depends on the object's speed, which is going to decrease rapidly because of the air resistance. So the force of air resistance won't be constant. There's no simple formula for this situation. If I had to work this out myself, I'd write a computer program to simulate the motion numerically in small steps, and then run it several times with different initial velocities, until I hit on the right velocity to produce a 10-cm drop.
Hmmm... 8.42 grams sounds like the weight of a bullet of some standard size. Maybe you can find tables somewhere for rifle-shooting, that give the required muzzle velocity in order to produce a specified drop at a specified distance. There might even be an approximate formula for this, probably based on actual measurements and some graph-fitting.
And we haven't even gotten to step (2) yet!