Could there be Roman ruins on the moon?

[carnyx]

At what stage in human evolution would it have been possible to get into space?

Here is a possible answer. Perfectly elastic tempered steel was known as far back as 400BC, so maybe the Greeks or the Romans could even have got to the moon.

So, what we want is;

1 a deep well with bedrock at the bottom, lined with a long tube made of cast iron or bronze

2 a set of sixteen tempered steel rods, all with the same diameter, whic wil provide a clear sliding fit to the well liner. Each rod will be half the length of the next, and each will have polished domed ends.

What you do, is to drop the longest rod down the well so that it hits the bedrock.

Then, at precise intervals, you drop each rod in descenting order of size, down the well.

Stand back, as the last and smallest rod comes out of the well and disappears up into space.

Given that the smallest rod weighs a kilogram, how deep must the well be in order to get this rod to come out of the well at an arbitrary 25,000 mph?

And, can it be done with 16 rods, or will we need more?

[carnyx]

Just to clarify, the steel rods act as a species of Newton's Cradle, involving an exchange of momentum.

M1.V1 = M2.V2=M3.V3 ... and so on

So if you imagine each rod is 1/2 M x 2V in relation to the next rod, then the smaller rod will recoil at twice the velocity of the previous collision.

[eamonnshute]

If you drop two balls, one small ball just above a much more massive ball, then if they are perfectly elastic the small ball will rebound with three times the speed, and therefore rise nine times as high! If you have a third ball which is much smaller still, it will rebound with seven times the speed and rise 49 times as high! The sequence is 1:3;7:15:31:63........

This would easily give escape velocity with 15 balls dropped from a modest height.

However, if the mass ratio is 2:1 then you do not get anything like the same result. If you do the sums you will find that he second rod will have 5/3 of its original velocity, and the next will have 23/9 (if my sums are correct).

Your assumption that the speed is doubled is incorrect, it is actually much less than that, and you would need a lot more than 16 rods.

[carnyx]

eammonshute

AFAIK the first rod comes to a halt against the bedrock and acts as a anvil for the second rod.
The velocity V of of all of the rods is determined by the depth of the well. So the second rod rebounds at V. The collision with third rod is thus at 2v, and so the third rod recoils at 4V .... and so on.

[eamonnshute]

If the second rod has mass m/2 and has speed v upwards when it collides with the third rod, which has mass m/4 and speed v downwards:
Before the collision the upwards momentum is mv/2 - mv/4 = mv/4
the difference in speed is 2v.

These will be the same after the collision.

The smaller mass will rise with speed 5v/3, and the larger will fall with speed v/3.
The upwards momentum is 5mv/12 - mv/6 = mv/4, as before.
The speed difference is 5v/3 + v/3 = 2v, as before.

[carnyx]

Thanks Eammon.

So rather than halving the mass of successive rods, what I need to do is to make each rod 33% of the mass of the previous rod, to get the optimum doubling of absolute velocity with each collision.

[eamonnshute]

For the optimum, each rod needs to be very much smaller than the next - 10% would be better. But then the last rod would be tiny while the first is enormous.

And that is before you consider the practical difficulties!

[carnyx]

Eammon

Here is an interesting toy ..

hyperphysics.phy-astr.gsu.edu/hbase/colsta.html#c5

[Progenitor A]

Interesting
But would it not be simpler just to drop a bloody great weight down the well that lands at the raised end of a see-saw, on the other end of which sits a small rocket shaped piece of iron. If th weight dropped is say 1000kg, should easily be able to calculate the height of the well.

[carnyx]

Ah! Good one!

"Give me a fulcrum ..."

And if an assymetric seesaw, at say 1000:1, was eaily constructed, we ought to say that evidence of the stone age might be found on the moon.

( .... but how could we tell?)

[Progenitor A]

Oct 29, 2010 16:59:21 GMT 1 carnyx said:

Ah! Good one!

"Give me a fulcrum ..."

And if an assymetric seesaw, at say 1000:1, was eaily constructed, we ought to say that evidence of the stone age might be found on the moon.

( .... but how could we tell?)

;D Really good!