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Why a man on the Moon can jump 21 times higher than on the Earth

  1. Oct 3, 2014 #1
    It's generally said that a moon walker should be able to jump six times higher on the moon, than he can on Earth, which sounds sensible since gravity is one sixth , but consider this.....

    Two men , one on the Earth, one on the moon, both bend their knees the same amount ready to do a 'standing' jump.
    They both start , and accelerate upwards.
    The earth man is pushing against the inertia of his mass and the downward force of his earth weight.
    The moon man is pushing against the inertia of his mass and the downward force of his moon weight.

    Clearly the moon man will have a higher velocity when his feet leave the ground than the earth man, and so will travel OVER six times higher.

    How much higher will depend on how long the acceleration zone is.

    When I do this I squat right down to the floor and can jump 30cm high. the acceleration zone is 90cm.

    The energy the earth man expends against the extra gravity iis 0.9 x( 1 - 1/6)g

    Equivalent to 0.9 x5/6 =75cm in earth gravity total jump =30 +75 =105cm

    This means he can jump 6.3meters on the moon!! 21 times higher
  2. jcsd
  3. Oct 3, 2014 #2

    Vanadium 50

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    Welcome to PF! I don't understand the purpose of your message. Is there a question in there? Or did you just want to show us an incorrect calculation?
  4. Oct 3, 2014 #3
    If you want a question then .... Is my logic flawed? Show me where the error is.
  5. Oct 3, 2014 #4


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    You are constructing a strange argument and it is based on arbitrary and irrelevant assumptions. There is no way you can get a valid answer that contradicts one that's based on Energy considerations. When you find (and it's very common for all of us) a nonsense answer, you need to scrutinise what you've done and look for the flaw.
    If the available energy (mgh) is the same in each case, and g is one sixth, the maximum achievable h will be six times what it is on Earth*. But there will be a problem in achieving this in practice. The impulse that the legs can deliver is matched to Earth conditions. On the Moon, it would be limited, without some help from a leverage system of some sort. What you seem to have done is to build a model that just gives the wrong answer. Time to think again and to reconsider what you mean, for instance, by "acceleration zone".
    * Bear in mind that millions of years of development of the muscular / skeletal system had produced a near-optimum utilisation of the muscles on Earth. The Energy based estimate will be surely over optimistic regarding possible performance on the Moon.
  6. Oct 3, 2014 #5
    Consider these two men , both with knees bent ready to push themselves into the air/space.
    Are you suggesting the man on the moon can't exert the same force as his twin on Earth?
  7. Oct 3, 2014 #6


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    Of course he can - but he is only applying that force for a shorter time as he will very soon be going as fast as his muscles will allow and as far as his skeleton will let him. That is why I introduced the term 'Impulse'. To get the full height, he must be able to apply his maximum force for a longer time - that would be by using a lever system (distance magnifier).
    Your argument is a bit along the lines of an argument that you should be able to throw a small ball bearing ten times further on Earth than you can throw a cricket ball (easy to disprove experimentally). Except with massive objects, your throwing ability is only limited by your arms and muscles and not by the object you are doing work on. That's why we use a rod to cast a fishing weight a lot further than we can throw it.
  8. Oct 3, 2014 #7


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    The result I get, based on the assumptions that I believe that oz93666 is using, matches his.

    Neglect air resistance. Assume that the force the man's legs generate is constant throughout the jump and does not depend on the magnitude of the man's acceleration. Assume that the jump from the fully crouched posture to when the feet leave the ground is 90 cm. Measure the height of the resulting jump from the point at which the feet leave the ground.

    On earth, we have that the 90 cm take-off results in a 30 cm jump. It is then clear that the take-off was at 1/3 g. One can obtain that result by equating the work done by the legs + gravity over the 90 cm take off and the negative work done by gravity alone over the resulting 30 cm jump.

    This means that the legs alone are producing a force equal to 1 1/3 of the man's Earth-weight.

    On the moon, we have legs producing a force of 1 1/3 of the man's Earth-weight and the moon pulling back with a force of 1/6 of the man's Earth-weight. The net is 7/6 of the man's Earth weight. This produces an acceleration of 7/6 of a g.

    Again, equating the work done by 7/6 of a g through a 90 cm stroke with the negative work done by 1/6 of a g through a jump of unknown height we get that the moon jump is 7 times 90 cm = 630 cm.

    Divide by 630 cm by 30 cm and one sees that the moon jump is indeed 21 times the height of the Earth jump -- under the stated assumptions.

    Sopie used a different implicit assumption (in particular that the height of the jump is measured from the bottom of the crouch rather than from the top) to reach an apparently contradictory conclusion.
  9. Oct 3, 2014 #8


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    You are assuming that there is no operational speed limit to the legs and muscles. Do you really think that you could throw a small (0.5kg ) mass as much as 21 times as high as you could make a standing jump, with a straight vertical push with your legs (with your body in a suitable upside down cradle arrangement)? You need to match your body to the required task if you want to approach the same amount of work done - and it is unlikely that you will be able to do more work than you can on Earth. If you could, then you would have to blame Mr Darwin for doing such a sloppy job with Earthbound body design!! Your argument is missing out a very important consideration.
  10. Oct 3, 2014 #9
    So you concede on the moon he will be going faster than on earth, so ' take off velocity' will be higher than on earth hence he can reach higher than 6 times earth jump, we just have to agree on how much higher.

    Yes , you're right , this is all dependent on being able to exert the same force at higher speed, I've a feeling this will be possible, as the speed is very moderate, and this can all be measured here on Earth in a gym.
  11. Oct 3, 2014 #10
    Are you referring here to throwing a cricket ball or similar with your arm?

    No there would be very little difference here because the 'acceleration zone' is short compared to the overall distance involve, it would be only slightly higher than six times earth hight. perhaps 6.1
  12. Oct 3, 2014 #11


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    I am pointing out the fact that, below a certain mass, there is very little, if any, advantage in reducing the load. In the case of throwing upwards with a push of the feet (like a standing jump on the Moon) there would be little chance of even achieving six times the height. Your 'acceleration zone' idea will only work if, in fact, the acceleration can be sustained over the whole distance. What evidence would you have of this?

    Of course he can and will be travelling faster. I maintain that he will be Energy Limited, though. There are enough instances on Earth where we find we are limited in how we can actually expend energy in a desired task and this can only be dealt with by using gears of some kind. A bicycle with gears can go much faster than a skateboarder on the flat, for this reason. The skateboarder can't actually add to his velocity once his legs are going as fast as possible (ignoring fancy leaning moves etc - which constitute another form of 'matching') Running down hill will result in an accident if you don't actually control your motion and the actual (safe and controlled) speed increase is never very great.

    I am taking on board the points you are making, though, and trying to reconcile the differences between our two models. The bit about the extra Kinetic Energy of the jumper when there is less weight force, makes sense. Certainly he is doing less work (1/6) in raising his body before he takes off and the remaining energy could be available as extra KE at the end of the muscle action. I am still questioning whether he could actually achieve the suggested higher speed at the end of the action. I imagine it would be easy to do some measurements with suitable gymn equipment. A simple test could be to do the experiment I suggested, involving a straight 'push' throw into the air with the feet. The height reached would indicate a maximum take off speed, on Moon or anywhere.
  13. Oct 3, 2014 #12


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    That does not follow, because there are serious limits to how quickly the jumper will be able to rotate his limbs and hence how effectively he will be able to take advantage of the (conjectured) opportunity to generate more energy during the jumping motion.

    There is a related statement that is true: It is possible to design a device that will reach a height greater than six times what it reaches on the earth. But it is far from clear that the human body is such a device.
  14. Oct 3, 2014 #13
    21 times? Air Jordan could jump 20 meters high on the moon then. No way .
  15. Oct 3, 2014 #14
    There is no suggestion the moon jumper is generating more energy than the earth jumper. If the force exerted by both jumpers is the same and the distance through which it operates is the same, then the energy is the same.
    The only question is will the fact that on the moon the feet of the jumper are moving away from the body at higher speed , effect the jumpers ability to exert the same force.

    Lets look at the speed at which the feet are travelling away from the body, at the point of maximum velocity, just before they leave the surface.

    on the earth the jump is 30cm................. m g h = 1/2 m v2 .3 x 9.81 x m = 1/2 m v2 v =2.426

    on moon IF jump if 21 times higher .........m g h = 1/2 m v2 .3 x 21 x9.81/6 x m= 1/2 m v2 v =4.538

    So even this higher speed is still very modest at 10mph.
    We can get an idea of the legs ability to push at high speeds by looking at martial arts kicks. Swinging kicks(roundhouse)have been recorded at over 120mph, but they are not applicable to our case ,we need a side kick, where the foot is pushed away from the body, it seems these have speeds of over 40mph which shows the muscles ability to act quickly, and exert force at much higher speeds than our case.
  16. Oct 3, 2014 #15
    Do you have any science or figures to support your position or is this just a 'feeling'.

    If Air Jordan could jump 95 cm in a standing jump , he could indeed get to 20meters. Thats very high jump on earth, are you sure he's not taking a run up? I haven't considered a running jump , makes things more complex....
  17. Oct 3, 2014 #16
    Kinesiology, I think that's the name of the science
  18. Oct 3, 2014 #17


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    Your calculations do not support this assertion. Let us re-run the numbers using the same [questionable] assumptions that went into the original 21 to 1 estimate.

    "Air Jordan" crouches 90 cm and manages a jump of 95 cm. That means that his acceleration during the jump must be 95/90 of a g. The force output by his legs must therefore be 1 g + 95/90 g or about about 2.06 g. On the moon this nets him about 1.9 g of vertical acceleration. 1.9 g over 90 cm during takeoff equates to 1/6 g over about 10.3 meters.

    He does not get to 20 meters. He only gets to 10 meters. The original claim of a 21 to 1 factor applies only to the special case of Joe Schmoe, not to the case of Air Jordan,.
  19. Oct 3, 2014 #18


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    While the common claim, of 6 times higher jumps on Moon, assumes those limits to be so small, that the take-off speeds will be identical on Moon and Earth. Both assumptions seem unrealistic and the truth is probably somewhere in the middle. It might not be 21 times higher, but could be more than those commonly stated 6 times.
  20. Oct 4, 2014 #19
    Yes ...your right , it's all got to do with the ratio of the acceleration zone to the hight jumped.
    Who's Air Jordan ? One of those lanky basketball players? I find it hard to imagine anyone from a squat could jump 95cm. If he's very tall then the acceleration zone , the amount he reduces his hight by squatting should be more, which means he can jump higher on moon.
    The figures I gave were for me, 5 foot 10 inches tall jump .3m acc zone .9m
  21. Oct 4, 2014 #20


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