Funny Astronauts Hammering Pole Into Moon Video
I love this video. During the Apollo 16 mission, Charles Duke dropped his hammer. What do you do next? You pick up the hammer, right? NOT SO EASY.
Why is this such a difficult task? It's a combination of the lower gravitational field on the surface of the moon along with the pressure inside the space suit. You see, humans are weird. We really work well on the surface of the Earth but at other places, we need some help - that's what the space suit does.
Air in a Bending Space Suit
Where I am right now, there is air all around me. It has an air pressure of one atmosphere (since I am at the bottom of one atmosphere of air). This is a pressure of about 105 Newtons per square meter (or about 14 psi). The Apollo space suit had an internal pressure of about 3.7 psi or about 2.6 x 104 N/m2. This is a high enough pressure for the human inside to still breath and do other normal human stuff.
If you look outside the space suit on the moon, there is no air and no air pressure. This causes a problem. It makes it difficult to bend your arms and stuff. Maybe I can illustrate this with a simple diagram. Suppose your arm is inside a cylindrical sleeve of a space suit. Next you bend your arm, what happens to the volume of air inside this sleeve?
Reducing the volume of air contained in the suit (even by just a little bit) will increase the pressure. This bending of the arm movement will require some effort on the part of the astronaut. No one ever said being an astronaut was easy.
Of course, you could make a hard shell space suit like NASA's AX-5.
This suit has joints that bend without changing the interior volume. It's easier to move around, but heavier with perhaps not as wide of a range of motion.
Video Analysis of a Moon Jump
Back to Charles Duke. If he just wants to pick up a hammer, he has to bend his knees. The more you bend your legs, the greater the force needed to compress the air in the suit. Even though he has a large mass with the space suit, the gravitational force on the moon is much smaller than on Earth. The weight alone is not enough to push him down to a kneeling position.
He needs a way to increase the force the ground pushes up on him. This increased force will then help him bend his legs. Actually, you can think of his legs as springs. His own weight isn't enough to compress these springs enough to get down low. His solution to this problem? Jump. If he hits the ground while moving, he will be changing his momentum. This means that the net force on him will not be zero. Here is a diagram.
In just the vertical direction, I can write the following two force equations for the two different cases:
Here I am using g to represent the local gravitational field (which is not 9.8 N/kg) and F G to represent the force the ground pushes up.
How about a video analysis? I love these kinds of videos. The quality isn't so great, but I'll take what I can get. But really, NASA knew what it was doing back then. They made a video with a tripod AND perpendicular to the desired motion. This video just begs for a video analysis. The only thing you need is some type of scale. I found that the life support system on the back has a length of 66 cm, so that's what I'm going with.
Using the free and awesome Tracker Video Analysis, I get the following plot of vertical position for one of these jumps.
I have fit a parabolic function to the jumping part of the motion. If the astronaut has a constant vertical acceleration, then I can write his position as a function of time using the kinematic equation:
Comparing this to equation that Tracker Video fits, you can see that the term in front of t 2 would be 1/2 the acceleration. This would give a lunar free fall acceleration of -1.542 m/s2. This is pretty close to the value 2 2listed on Wikipedia at 1.62 m/s2.
Ok, but what about the acceleration while the astronaut is landing on the ground? Using the same idea, I can fit a parabolic function 1.34 m/s2 (in the upward direction). So, what is the ratio of the force on the astronaut compared to just standing there (with zero acceleration)?
With this little jump, he almost doubled the force the ground exerts on him. Of course, he still didn't get the hammer.
Source: https://www.wired.com/2013/12/how-do-you-pick-up-something-on-the-moon/
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