Strobing.
Neat though.
VB
R4 Puzzle for the day this morning.
If Neil Armstrong could jump 50 cm vertically on earth how high could he have jumped on the moon (using the same amount of energy) assuming the moon has 1/6 the gravitational pull of the earth?
Is there a reason why this wouldn’t be 3 Meters? I was lying in bed this morning trying to mentally drop the numbers into the laws of motion (SUVAT) & it was coming out with that figure but it seemed too easy. Couldn’t remember if the d squared part of the gravitational constant formula would be making a difference.
could he jump 50cm on earth in a spacesuit?
I don’t know. Probably not but the issue is would he jump 6x as high?
Gravitational potential energy is mgh. Mass is the same, g is a sixth so h will be six times, so 3m, yeah.
In practice it doesn’t because the d in question is the distance from Armstrong to the centre of the moon. This distance varies by only a very tiny percentage between the moon’s surface and the highest point of Armstrong’s jump (3m higher up). So even though the force goes like the reciprocal of d squared it really doesn’t change detectably. What this boils down to is that the acceleration due to gravity in Adam’s formula, g, can be regarded as a constant.
Another negligible thing (but maybe less negligible ?) is that there’s no air resistance on the moon.
Probably the biggest difference would be that when Armstrong’s leg muscles contract to push him upwards the force that they generate would be working against some combination of his weight and his inertia. These two would limit his acceleration. His inertia depends only on his mass, which is the same on the earth and on the moon. But his weight depends on his mass and on the local gravity, so that would be different between the earth and the moon. This means that his motion while his feet were still on the ground would be different in the two circumstances and that means, in turn, that in general he wouldn’t leave the ground at the same speed in the two cases. To make the physics easy we were instructed to assume that he would leave with the same KE, which amounts to saying that he would leave with the same speed. But that’s an oversimplification.
VB
2 Likes
Fun on the moon
Yeah assuming his muscles are capable of a steady force, on the Moon he would take off earlier. Since the impulse (in Newton seconds) is equal to the momentum (mass times velocity), on the Moon he would have a lower take-off velocity.
As ever with these kinds of questions, the interesting parts are when you think about the simplifying assumptions!
1 Like
Interesting, but not really true. We know a great deal about gravity which isn’t wrong. The comments are worth reading. I agree with the one that says attacking our understanding of gravity at a fundamental level without mentioning general relativity* is missing a great deal of the picture out (almost all of it, in fact).
It is true that gravity is fantastically weak compared to the three other forces, and we haven’t convincingly quantised it yet, but that doesn’t mean it isn’t a force. It’s a fantastically weak unquantised (yet) force.
VB
*“Spacetime tells matter how to move, matter tells spacetime how to curve.” - John Wheeler
1 Like
Oi! I never said that 
5 Likes
Sorry, I should have said John Archibald Wheeler (if that’s you too then I’m stuck).
Archibald wrote a good book called Spacetime Physics which can be quite a help if you don’t want to pitch straight into the tough maths of relativity. Apparently the second edition is poor though. Here’s the start of the first edition http://www.eftaylor.com/pub/stp/STP1stEdThruP20.pdf (the rest of the book has been scanned in on the same website). Fig 7 is an ad for a good-sized piece of building work.
VB
1 Like
Almost as bad, John, Ernest, Wheeler 
please don’t tell anyone 
Keeping it quiet might cause a good deal of trouble
VB
1 Like
I’m just surprised that there is an Ernest builder out there.
1 Like
Was the greatest genius of Einstein the ability to move from “forces are mediated by tiny particles”, which everyone understood, to “spacetime, it’s all curvy”, which made everyone say, “dafuq?”? And still it’s hard to accept, a century later.
It’s just marvellous tbh.
1 Like
That was one of them. When I first learned that whether something looks like electricity or looks like magnetism depends on which reference frame you’re in Classical electromagnetism and special relativity - Wikipedia I think I pretty much said “dafuq?” too. I knew electricity and magnetism were linked but not that they really were the same thing just experienced from a different point (OK, frame) of view. And that’s just special relativity !
VB