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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!"

Connotations are bad science, no?

If the bag said "on the Moon" instead of "in space", the complaint would be a lot more pedantic.

"On the Moon" is a subset location of "in space". Everything is technically "in space". Obviously the writer meant "on the Moon" and "on Earth", but didn't say that, hence the bad science.

You *can* jump six times higher in space.

Consider a person who can jump 1 foot high on earth. If that person were to jump from a space platform, assuming the platform itself had no gravity, then at some time t0 they would be at 0f, at t1 they would be at 1 foot, just like on earth, on up to t6, when they would be at 6ft, or 6 times higher than their earth jump.

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

Err, shes clearly jumping off the moon in the illustration. I think that the connotation is obvious. When did you become the web's Andy Rooney?

My son's book, "Machines As Big As Monsters," claims that work on the Space Station is taking place "millions of miles" out in space.

Edited by author 01-29-2007 06:53 AM
Bisons and squirrels can sing before hibernating? Quality!

Good catch. My husband and I noticed something similiar on the children's channel, Noggin. They suggested that bison and squirrels hibernated during one of their interval songs. What kind of information is that to be giving to a 2 year old?

And we all know that no man ever set foot on the moon.


THE DELUSIONS END NOW!

The claim on the McDonald's bag isn't right even on the moon. 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, which makes for a much smaller jump, as the center of gravity is somewhere in your chest or abdomen when standing.

Arthur C. Clarke did a interesting lecture, or possibly article, in which he debunked this, and calculated approximately how high the current world record holder for the high jump could jump on the moon. Can anyone find a link to the transcript on the web somewhere?

Is this before or after eating a happy meal?

If you jump in orbit, you'll just end up in a more elliptical orbit, which you'd experience as a rise followed by a fall back towards the item you jumped from.

I saw one that said goldfish only have a 3 sec memory but thats wrong its about 18 months

This was too interesting to pass up.

Given v[0] (initial jump velocity) and v[1] (apex, v=0), and uniform acceleration (a), we can use the equation

t = (v[1] - v[0]) / a

to get our time. So a jump on the moon will take six times longer than on earth. For distance we can use:

d = v[avg] * t
v[avg] = (v[1] - v[0]) / 2

Therefore our jump will distance (height) will increase six times on the moon given an equal initial velocity.

But will our initial velocities be equal? Solving for v[0] is simply v[0] = a * t, but solving for those two variables proves impossible. The pre-liftoff time varies dramatically because of the decreased load (weight), and calculating muscle speed at varying loads is really a matter of anatomy and physiology. The pre-liftoff acceleration also varies largly, especially because the "escape acceleration" (acceleration > g in order to lift off) does not scale linearly as mass and strength vary.

So to answer the problem, if you jump the same speed as on earth, you will jump six times as high. But in reality it matters how much you weigh, how strong you are, how quickly your muscles move, etc...

And yes, I realize that in my example, if you jumped at 32 feet per second, that would mean your feet are 16 feet in the air, which not even Michael Jordan could do. But it was just an example to illustrate how the speed of the jump has to be divided by g to get the time in the air (since acceleration is change in speed per unit time).

Did no one else here take high-school physics? ;]

Edited by author 01-29-2007 02:56 AM
I did some calculations and got I could jump 7.5 times as high on the moon.
Assumed:
a)leg recoil before jump = 0.2 m
b)I can jump = 0.4 m
c)legs apply a constant force during the jump

d) F(legs) + F(gravity) = ma
e) get lift off velocity by integrating over my leg recoil distance
f) Use energy conservation, knowing everything but F(legs)
g) On earth this gives my leg force to be about 3 g's worth
e) assume same leg force on moon
f) assume same prejump recoil distance
g) get new lift off velocity on moon
h) Use conservation of energy to get height = ~ 3m = 7.5 earth distance

"Well, if you jumped off anything in space, wouldn't you eventually land back on it again, theoretically?"

Not if you jumped off at escape velocity or higher. Not gonna happen off the earth or moon (you'd need to jump at thousands of miles per hour), but you could totally escape-jump off of smaller things like an asteroid or space station, which are not massive enough to have escape velocities higher than jumping speed.

Stefan Jones is right, too: If you're in orbit around a massive celestial body and jump off something else that's also in orbit, you and the other thing would keep going around in orbit, but in slightly different orbits. Depending on the relative masses, and in the direction you jumped off (along the direction of the orbit? Perpendicular to it, to the side? Or in the up/down direction?), you could even end up hitting your platform after as little as half an orbit, if the resulting orbits cross each other and have similar inclinations and apogees/perigees.

"...given that your weight on the moon is roughly one sixth that of your weight on the earth, does that necessarily mean you'd be able to jump six times higher on the moon than you can on earth? I have a hunch that's not necessarily so"

The acceleration due to gravity is one sixth what it is on earth. So if you jump up at the same speed (ignoring cumbersome spacesuits and whatnot), then you spend six times longer in the air (or in the vacuum... six times longer off the ground). In that time, your velocity profile over time is the same as it would be on earth (ignoring air resistance), just stretched out in time 6 times. If you're going the same speed (or the same speed profile) but for six times as long, then you're off the ground six times higher.

The height reached by a projectile is

1/2 of V2 over A

or one half of the speed squared divided by g. ("A" is the acceleration which is G). So if g is divided by six, then the height gets multiplied by 6.

Proof of the above formula:

Time to maximum height = time until speed goes to zero = speed divided by acceleration = V/A (e.g. if you jump off at 32 feet per second, it will take one second at Earth gravity before you've lost your speed and are at the top of the jump)

Max height Y = 1/2 of A times T squared (e.g. if you jump at 32 feet per second and smoothly decelerate to 0 feet per second, then on average over that time you were going up at 16 feet per second. Acceleration times time gives total change in speed. Divide that by two and you get the average speed, assuming the final speed (when you reach the top of the jump) is zero. Multiply that by time and you get the distance).

So if T=V/A and Y=1/2 AT2, then A=V/T and y = 1/2 VT = 1/2 VV/A

which is half of the square of your jumping speed, divided by the acceleration of gravity.

So with one sixth the gravity you jump six times as high. But if you could just jump six times as fast (even here on Earth) you'd go up 36 times higher...

Does Homer Simpson have to come and remind you all about the Air In Space Museum?

  You could fit a whole lot more nonsense onto a Happy Meal bag. Hey, why not "I'm Lovin' It" in, like, eight hundred different languages? Yeesh.

  If we're talking about deep space, then no, jumping isn't relevant. Floating, drifting, wafting... lots of other phenomena may apply. But if we're talking about the moon, you couldn't jump six times what you could on Earth. Not a chance. The difference in gravity is only one factor to consider. Let's not forget all the heavy equipment you'd be wearing.

  All hail the new Mayor McCheese. Scienterrific!

McDonalds: Rots Your Body, Rots Your Mind.

i like space

Well, if you jumped off anything in space, wouldn't you eventually land back on it again, theoretically?

Gravitational potential energy = height * weight. Thus, if weight-on-moon is 1/6th of weight-on-earth, then a jump with the same energy will climb to a height 6 times as high.

I passed high school entirely on information I gained from McDonald's Happy Meal bags, as well as by consuming large amounts of cold medicine and selling information to the administrators.

They were going to let me shoot the big death missiles from submarines in the Navy.

But my McDonald's physique caused me to sustain severe injuries while in training, so they sent me home.

Don't worry, a guy with Hallucinogen persisting perception disorder got my job instead.

Welcome to my world.

Here's my question for the physics-non-challenged among us:

Assuming they meant "on the moon," and not "in space," and given that your weight on the moon is roughly one sixth that of your weight on the earth...does that necessarily mean you'd be able to jump six times higher on the moon than you can on earth?

I have a hunch that's not necessarily so, but I don't have the physics or mathematical chops to say one way or the other.

gravitational force = G*M1*M2/R^2 where G is the gravitational constant, M1 and M2 are the masses of the two bodies and R is the distance between the centers of mass of the two bodies. The ratio of gravitational forces on a person (M1) on the earth and on the moon is (G*M1*Mearth/Rearth^2)/(G*M1*Mmoon/Rmoon^2) or, simplified, (Mearth/Rearth^2)*(Rmoon^2/Mmoon). This is (5.9742e24/6373^2)*(1737^2/7.3466e22) with units in km and kg. Do the math (http://www.google.com/search?hl=en&q=%285....6e22%29&btnG=Search) and, voila, the force on the surface of the earth is 6.04 times the force on the surface of the moon.

Of course, the McDonalds statement is perfectly true. You can in fact jump six times as high in space, or ten times, or fifty times... the lack of gravity makes for wonderful jumping. Of course, getting back down, that's another matter. By the way, that whole 'need spacesuit, no air... gasp' scenario is of course an urban myth. Anyone who has gone up in a tall building can tell you that air continues to exist as you go towards space. NASA suits were just a misguided attempt to influence the fashion industry.

"Find a spot in the pool where your shoulders are just out of the water. Now hop like a bunny. This is how it feels to walk on the moon! Try it, it's fun!"

Bleh. At least, that's the way I would've written that fun fact. Besides, the thought of dozens of kids moonwalking/bunny-hopping in a pool fills me with nerdy glee.

The two WORST examples of quasi-science I've seen were both "Jamba Juice" ephemera:

* What appeared to be a employee-generated list of the benefits of wheat grass. Among other claims: If you put wheat grass between you and a TV, it will absorb harmful radiation. DUHHHH!

* An article in the give-away Jamba Juice newsletter quoted some new-age wonk who somehow conflated photons and electrons and thought fruit contained sun energy. Not "nutrients created by photosynthesis" but some kind of mystical photonic sun energy. That your body's atoms screamed out for. DUH! DUHHHHH!

Of course, all of our indignity and outrage won't change things. We're talking about epemera generated by advertising copywriters who got a BA in Communications.

You are incredibly smart. Kudos to you!

They totally mean the moon. Think of all those videos with Neil Armstrong.

It's not exactly surprising that the science educations of McDonald's Happy Meal copywriters is imperfect.

It must have meant 'on a space ship,' notice our female friend isn't wearing any sort of space suit.

As we all know, it's physically impossible to build a space ship with rooms any taller than, say, 12 feet high. I'm six feet tall and can normally jump 1 foot in the air. In my space ship I'd be able to jump six feet in the air at which point my head would hit the ceiling. This, of course, is six times the height I can normally jump.

Never question a McDonald's fun fact.

Lots of bad science and urban myths perpetuated in kids books. I recently read a book to my child that claimed you can see the Great Wall of China from space. Not true ( though a satellite can apparently).

I also remember reading a book about Canada that gave you the impression that we all live in igloos and fight Caribou.

Checking on the accuracy of kids science books would probably be a good study for someone.

Hmm.. If you jumped in space, without a spacesuit (like the girl on the bag), I'd be more worried about where my next breath was coming from, than when I'd stop.

Today, "in Space" still means "in a Spaceship" or "in a Spacesuit"

Why were you eating at McDonald's anyway?

I think it's quite apparent they meant the moon, but it says a lot about what they think about the intelligence of kids. Or it says a lot about the intelligence of the goofball who wrote that. Do they think kids would be confused by the phrase 'on the moon'? I doubt it's a room issue, as 'on the moon' is only 2 letters longer than 'in space'.

I was assuming deep space, no orbits. It wouldn't take much of a push to reach escape velocity from a platform.

I think Mark is right; they were thinking of the Moon.

As for "just keep going," it depends. If the platform was in an orbit around the Earth, you'd just end up in a slightly different orbit. (As would the platform . . . equal and opposite reactions and all that.) Unless you had really good legs, they you'd end up in orbit around the Sun. Or really, really good legs, and you' be drifting in a big orbit around the galaxy.

Try fitting that on a Happy Meal bag.