# Annoyed astronaut problem

Two disgruntled astronauts in identical space suits are out on a space walk around the ISS. They manage to annoy one another to the point of wanting to impart physical harm. The Russian, in his fury, grabs hold of a small 0.5kg meteor and hurls it at the American with a force of 500N. At the same time, the Yank scoops a large handfull of gravel from the tail of a passing comet, also 0.5kg’s worth, and flings it at the Russian with an identical force of 500N. Both astronauts release their projectiles at the same instant.

Who will be struck first? Who’s visor is the most likely to break?

Mintaka

Wouldn’t each astronaut move backwards from the force of their throw? And therefore move away from each other and their respective projectiles at the same speed? Hey - I’m a muso and know very little about physics - does the answer depend on whose life-line-cable thingy is the shortest? And is force not related to mass rather than weight if you are in space? Eish - I dunno.

You first need to clarify what it means “to throw [something] with a force of 500 N (Newtons)” because it’s physically meaningless unless you mean 500 J (Joules) or also tell us the time interval for which the force is applied to the projectile.

If indeed you mean an energy of 500 J, the guy throwing the single piece is likely to be hit first because the individual gravel bits will have a distribution of velocities, some bits travelling faster and others slower than the average for the whole handful. On the other hand, the gravel thrower’s visor is more likely to be broken because the energy of the single chunk is concentrated in a single mass, rather than spread over lots of little pieces. Shooting someone twenty times with a pellet gun is less likely to kill them than shooting them once with a .45.

'Luthon64

Thrown with a force of 500N acting over t seconds in each case. (Hopefully it will cancel out somewhere).

the guy throwing the single piece is likely to be hit first because the individual gravel bits will have a distribution of velocities

Interesting - will the smaller bits travel quicker? Will the accelerating force during the throw be “shared” (maybe unequally) between the gravel bits?

Mintaka

If the force was equally applied to the small bits, would not those with less mass be accelerated more ( a=F/m ) thus go a bit quicker, even bumping into others? Possibly the mechanics of throwing wif your hand and fingers might mean an unequal distribution of force?

A shotgun blast seems to have a leader-of-the-pack:

I think it is more likely that the forces would be nearly proportional to the respective masses of the grains, giving them similar but not identical acceleration.

Okay, so the essential message is that the meteor chunk and the handful of gravel (1) each have the same total mass, and (2) are each thrown with the same total energy. (As a pedantic aside, one could just as well have specified the total distance through which the force acts.) The total energy doesn’t cancel out. It falls away as a factor in a relative sense when comparing the two scenarios, but it remains important in an absolute sense for deciding what the nett damage will be.

I think you misunderstood my meaning. The average velocity of all the bits taken together will be the same as that of the single meteor chunk (their masses being the same and ignoring differences in rotational energies). Owing to differential friction between individual gravel grains and the launching hand (as well as differential rotational energies – again ignored), some of the grains will have slightly more energy and some slightly less than their theoretical, perfectly-balanced allotment, which differences would manifest as differences in velocity. That is, a few of the bits would travel faster than the single chunk, arriving at their target earlier, while others would travel slower, arriving later.

If desired, I can give the precise mathematical formulations that the situation would be subject to. (The answer I provide is hardly definitive. The issue would, really, need to be settled empirically.)

The point is that because a few of the gravel grains have a higher velocity than the single chunk, they would hit their target earlier, whereas the single chunk carries all of the energy in a single bundle and is therefore more likely to do serious damage (assuming the throwers’ aims are very accurate).

I hope the above adequately clarifies the situation. Please feel free to ask more if it doesn’t.

'Luthon64

The gravel should win. A few pebbles will strike the chunk thereby lessening the force or maybe even change it’s direction.

So what is the answer, Mintaka?

Tweefo, I didn’t have the answer when posting the problem, mate! :-\ But the explanation above sounds feasible … i.e. some fraction of the gravel particles will travel quicker than the single lump of meteorite, with the latter capable of doing more damage.

Mintaka