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Here's some stuff that I found printed on my McDonald's Happy Meal bag in February 2007. Is it me, or does everyone like their kids going around saying these things???

"Hi Ho Kracken!"
"cream-filled sock puppet?"
"my slimy little friend that I love to play with!"

What is McDonald's thinking?!?!? Is this how kids talk nowadays??? I wonder why?

So chemgeek thinks that a person accelerates up at about 1g while jumping. I think it's more like 3g.

If he's right and it's 1g, then the extra 5/6 g of being on the moon (and not having to fight earth's gravity while pushing off from the ground) would greatly increase your jumping speed. But if I'm right and it's 3 or 4g, then the extra 5/6 g from being on the moon probably won't add that much.

Now I want to try and think of a simple way to find out how fast we accelerate while we push off from the ground. It could be calculated from the ratios of how much we crouch to how high we go in the air, for example. But without Mythbusters-style high-speed footage of someone jumping in front of a wall painted in horizontal black-and-white bands, it's hard to come up with a number that's any better than one we just make up.

See how much good (ish) science this Happy Meal bag has stimulated? ;]

You people gave me a headache.

I gave the problem some thought while I couldn't sleep last night and came up with some model numbers: Bernardo is right that you're fighting both inertia and gravity when jumping and that inertia doesn't change. But if you look at a average poor jumper doing a jump from a standstill, he will probably crouch (moving his center of gravity -0.5m) and then jump so that his feet are 0.5m off the ground. So he will have to spend the same energy producing impulse for his jump that he has to use just to get up from the crouch (i.e. whatever it takes to move your center of gravity up half a meter).

On the moon, assuming everything else stays the same (no bulky spacesuits etc.) the work just to get up from the crouch decreases to 1/6, so he will have 1 5/6 times the work left for the actual jumping. So if the force that his muscles can generate is constant and the 0.5m that he crouched before the jump stay constant, he should end up with almost twice the lift-off velocity compared to earth. Of course that assumes that his muscels can contract fast enough to actually produce the speed.

Anyway, shouldn't the model jumper be able to jump almost 12x the heigth than on earth. Maybe my high school physics is so rusty that I messed up somewhere, but I don't think I did.

So, the better you are at jumping the less you benefit from the lower gravity, because the fraction of work you spend on just moving your ass, instead of accelerating, will be lower.

The airplane would never take off.. it's tires would fail first... Oh wait different problem.

I had the same conclusion as jm: you *can* jump six times higher in space; you just don't know when you'll stop.

Not nearly as bad as the science I found on this Pasta Pomodoro kid's menu:
http://flickr.com/photos/numlok/373696182/

Couldn't we assume that the girl is in a pressurized McDonald's on the moon, and therefore doesn't need to wear a spacesuit?
-q

I blogged this bag way back in May 2006. I can't believe I was eight months ahead of Boing Boing.

http://zerosink.blogspot.com/2006_05_01_archive.html

Edited by author 01-29-2007 01:56 PM
"I was assuming deep space, no orbits. It wouldn't take much of a push to reach escape velocity from a platform."

:)

But QuickTopic? Seriously? After all these years? (It still sucks.)

Stevarino: "But will our initial velocities be equal?"

Good point. Part of the force made by our muscles while jumping is to overcome our weight. Most of the force, however, is to overcome our inertia (since we accelerate up at more than 1G while jumping). Remember that, on the moon, you might have less gravity to overcome, but you have just as much inertia.

If, while jumping up, your body accelerates up at 3g, then on the moon it would be about 3 5/6 g, but over a shorter period of time (same distance, if you jump the same way). So yeah, you should leave the ground a little faster, but not much. One way to find out would be for someone to wear a harness that allows them to hang from a giant pendulum while lying down horizontally, and then have them push off from a wall as hard as they can. Their speed would be closer to moon jumping speed than vertical earth jumping speed.

"If you jump in orbit, you'll just end up in a more elliptical orbit"

Not necessarily. If you jump in orbit in the upwards/downwards direction, or along the direction of the orbit, you'll end up in a more elliptical orbit (or in a LESS elliptical orbit, if you time it right). But if you jump in the sideways direction with some component along the direction of the orbit, you might just change your inclination (i.e. you might just change your orbital axis, but keep the same orbit shape, just tilted differently).

"Does the word "Jump" also incorporate the word "Land"?"

Neglecting air resistance, you always land at the same speed you left the ground, but going in the opposite direction.

"Again, all of you people saying that you can jump six times higher on the moon are WRONG... you WOULDN'T be wearing heavy boots, a space helmet, padded jumpsuit, and oxygen tanks."

All right. Then, on the moon while wearing a spacesuit, you can jump six times higher than you can jump on earth while wearing a spacesuit. Well, a little more than 6 times since your jumping speed will be a little higher (less weight, same inertia) and you'd have no air resistance.

"You can't actually jump six times as high as on earth, you can only raise your center of gravity by six times as much as on earth"

Hopefully, when my center of gravity moves by some distance, the rest of my body follows! If my center of gravity goes up by a foot, my feet also go up by a foot, and so does my head. If my center of gravity goes up six feet, so do my feet, and so does my head. Unless I try to perform a flip or something. And yes, I know that the athletes who do high-jumps arc their bodies so that their bodies go over the bar even though their CG might not. But still, it would all be 6x as high (or a little more) on the moon as on the earth.

"The bag doesn't say anything about what happens after time t6."

Good point... The bag is right after all... ;)

Does the word "Jump" also incorporate the word "Land"?

  Again, all of you people saying that you can jump six times higher on the moon are WRONG. If you were wearing the same clothes on Earth as on the moon, that might be possible. But on Earth you'd likely be wearing tennis shoes, shorts, and a t-shirt. Or jeans, dress shirt, a tie, a dinner jacket, and scuffed-up loafers. Or a party dress. But you WOULDN'T be wearing heavy boots, a space helmet, padded jumpsuit, and oxygen tanks. That's all there is to it.

It should say - "In space no one can hear you scream that your food is toxic!"