question and answer thread.

When thinking about forces it's important to remember that you may not be aware of all the forces being applied. Here are a couple of examples that might help.

First imagine you’re standing on solid flat ground and you try to push a 3 kg box. It shouldn't be that hard to move. Now try and push a 300 kg box. That should be almost impossible to move. Now imagine doing this on a frozen lake. If you tried to push the 300 kg box what would happen? The box wouldn't move you would. You would be pushed back away from the box. When you push something, something has to be pushing on you if you don't move. Many times the thing pushing on you is the earth. It's hard to see that when you’re on solid ground but on the ice it becomes much more apparent.

The next question might be if the earth is pushing back why doesn’t it move? Well it does. Now this will really mess with your head but like the good Doctor Luz said Force=mass*acceleration. If you apply a 10 Newton (N) force to an object the earth applies a 10N force to you (assuming you don't move and the object does.) Since the earth is so large compared to the object its acceleration will be very small. And usually completely insignificant. I think I'm starting to ramble now so I'll shut up.

Does that help? If not let me know and I'll try to explain a little better.

-Ben

To complete the example of bmacri, if you push a 3 kg box hard enough while standing on ice, it will move forward, but you will also move a little backward. This shows the the box, even small, applies some reactive force upon you.

Have your child put on some roller blades and throw something heavy. Have someone behind him (or her) though ready to catch him (or her) b/c they could easily fall. But the point is that both the object thrown and your child will move -- just in an opposite direction. Your child pushes on the object, thus it moves. The object pushes back on your child thus he (or she) moves. They move in the opposite direction.

I tutored for university physics for 3 years. Let me know if you need some more examples or if you have some other questions.

- Kevin

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The next question might be if the earth is pushing back why doesn’t it move? Well it does. Now this will really mess with your head but like the good Doctor Luz said Force=mass*acceleration. If you apply a 10 Newton (N) force to an object the earth applies a 10N force to you (assuming you don't move and the object does.) Since the earth is so large compared to the object its acceleration will be very small. And usually completely insignificant. I think I'm starting to ramble now so I'll shut up.

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I actually worked this out in my head once. I believe the earth's center of mass moves a distance of only a fraction of a width of a proton (very small fraction if I remember correctly) when we throw a heavy object as far as we can. Just in case anyone was wondering.

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Originally posted by KevinHall
I actually worked this out in my head once. I believe the earth's center of mass moves a distance of only a fraction of a width of a proton (very small fraction if I remember correctly) when we throw a heavy object as far as we can. Just in case anyone was wondering.

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And as it is likely enough that other people will throw the same kind of object in the opposite direction somewhere on Earth, it gives an even weaker result... :p

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Originally posted by Elrond
And as it is likely enough that other people will throw the same kind of object in the opposite direction somewhere on Earth, it gives an even weaker result... :p

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And given that the earth is not truely a rigid object, the effect that you have on the earth will be mostly local decaying with distance rather quickly (within a couple of yards of where you stand for any significant measurements). ;)

So if everyone on one side of the earth was to jump up and down at the same time would the earth go flying off into space? Or better yet how many people jumping up and down on the same side of the earth would it take for the earth to be thrown out of orbit?

I'm not really expecting an anwser it's just a question that seems to come up everytime when a discusion like this occures.

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Originally posted by bmacri
So if everyone on one side of the earth was to jump up and down at the same time would the earth go flying off into space? Or better yet how many people jumping up and down on the same side of the earth would it take for the earth to be thrown out of orbit?

I'm not really expecting an anwser it's just a question that seems to come up everytime when a discusion like this occures.

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To be calculated, but it might be more that the number of people that have ever lived on Earth so far. It means that the risk is small enough ;) :p :D

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Originally posted by bmacri
So if everyone on one side of the earth was to jump up and down at the same time would the earth go flying off into space?

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No. People (even collectively) do have the strength to overcome the gravity of the earth. The center of mass of the earth would follow the same orbit around the sun and in one second, everything would be back to normal.

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Originally posted by bmacri
Or better yet how many people jumping up and down on the same side of the earth would it take for the earth to be thrown out of orbit?

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It would take an aweful lot. You would need the collective mass of people to much greater (thrown out of orbit) than the mass of the earth. Say the average person weighs 100kg (perhaps a little on the heavy side) and "much greater" would be a factor of at least 100. Then we have 100*(6e24 kg / 100kg) = 6e24 people or 6 septillion people (6 trillion trillion people).

- Kevin

1
11
21
1211
111221
312211
13112221

What row of numbers comes next?

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Originally posted by KevinHall
1
11
21
1211
111221
312211
13112221

What row of numbers comes next?

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1113213211
Better yet, how 'bout prove that there can never be a 4 in this sequence.

You're right. There can never be a 4 in the sequence because the first instance of any number other than 1 will be preceded by a 1 in the next sequence. Thus the longest chain of a single number will be "111" which will become "31" in the next line. Since "111" is the longest sequence, there will never be a "41" or "4x" (fill in the x). Ok, so this is not a proof that would pass in a set theory class, but I think it should do for this thread.

- Kevin

Now how about the following (this one I actually created myself -- hope it isn't too hard):

C15
2046
5652
133332

What line comes next? Let me know if you need a hint.

Ooops... That last one is not answerable. Here is something identical in design, but that is answerable:

D15
1A24
5007
40232

What line comes next? (Extra credit if you can tell me why the puzzle in the last post is not answerable.) Again, let me know if you need a hint.

- Kevin

Ok, here is a hint. Each line is a representation of the number two thousand five hundred sixty seven.

My guess is
101000000111