So my 7-year old asked me this and as much as I would love to be able to give him a proper answer, I couldn’t.
Does ball A (in space) float away, taking ball B (above earth’s surface) with it? Will the balls stay somewhat fixed or will ball B force ball A down?
In: Physics
Let’s make a few assumption to make this whole problem possible then lets just… Map it out?
First, we’ll assume that both balls have the same weight and that the rope is weightless (just to make things simpler). We’ll also assume that the rope is unbreakable. Earth ball (EB) is the one on the surface and Space ball (SB) is the one in space.
First thing, the earth has a gravitational pull. basically, anything that get close enough is attracted by the earth. The closer, the stronger the attraction. For now we’ll ignore the other big force that will matter. We’ll just focus on gravity.
Gravity is applying a force on both balls. EB is taking a stronger force than SB by virtue of it being closer to the ground. As long as EB does not rest on the ground it’ll try and get closer, giving part of its acceleration to SB. SB, unless really far away is also getting attracted but to a lesser degree. Since the rope is unbreakable, EB will be slowed down because it’ll be giving some of its acceleration to get SB moving. EB will thus be moving slower but still moving toward the ground while SB will be moving faster by stealing some of EB’s acceleration. Basically, if there is absolutely no other force at work, EB and SB are bound to both end up on earth.
But there are other forces. The first one is gravity from other astral things. Stars, planets, comets, moons, etc. It’s simply impossible to evaluate. So we will acknowledge their existence, but ignore them.
There is though one other force that we CAN take into account somewhat reliably. Centrifugal force. The earth is spinning. Centrifugal force apply to both balls again. but this time, the further you are from the center of rotation, the more acceleration you get. So this time, SB is getting a lot of force whereas EB isn’t getting much. it’s actually low enough that gravity is by itself enough to hold EB from its own centrifugal force. But since SB is much further out, it’s likely that SB will take a stronger centrifugal force than gravity will pull. SB will try to leave for space. In it, it’ll try to drag EB.
And that is the result. Basically, the further the ball, the stronger the centrifugal force pulling balls away. The closer the ball, the stronger the gravity pulling balls closer. Which mean that the real question become… How long the rope is? If the rope is long enough, centrifugal force will apply enough energy to SB that it’ll drag EB away. If the rope is short enough, gravity will overpower the centrifugal force and EB will drag SB back. If the rope is just the right length, gravity and centrifugal force will simply counter each other leaving the balls somewhat where they are
I’ll assume you’ll want to explain these concept to your child. You’ll probably want to simply try and explain what centrifugal force is by tying a ball on a rope. Show him that the ball always fall toward the earth. That’s gravity. Then start spinning the ball on a rope. That’s centrifugal force. If you do it properly, the ball will rise despite gravity. Proof that it’s powerful enough to counter gravity. I have no idea how to make him correlate the rope length with the gravity force since in our little test, we’re willingly exaggerating the force for demonstration.
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