Exploring the Physics of Jumping: One Leg vs. Two Leg

[idea2000]

Hi,

I was playing basketball the other day and I noticed something that puzzled me. Why is it that when I jump off of one leg I jump just as high as when I jump off of two? Shouldn't I be exerting 2x the force when jumping off of two legs? And if I am exerting 2x the force, shouldn't I be jumping much higher? Any response on this question is greatly appreciated...

 

[berkeman]

The key difference is what you do with your other leg. Try this, jump first off of both legs together. Then jump off of one leg, but do not move your other leg -- just keep it still. You jump less, correct? Now jump the way you normally do with one leg, where you are pulling up the other leg as you jump. This is imparting upward momentum to it and your body, which helps you to get as high as you can.

It's like the jumping motion you use in volleyball, to get as much height as possible for spiking or blocking. You take a quick step or two forward, land on both feet in a part squat with your arms down, and then spring up with both legs as you raise your arms quickly. You are adding extra upward momentum to your arms and body by doing this, and that extra upward momentum carries you higher than if you had done nothing with your arms.

 

[Meir Achuz]

Jumping with both legs is forbidden in the high jump competition.
The first jump over 7 feet was done with both legs and was disqualified.

 

[berkeman]

Jumping with both legs is forbidden in the high jump competition.
The first jump over 7 feet was done with both legs and was disqualified.

How strange. I couldn't believe that there would be such a rule, but you're right!

http://en.wikipedia.org/wiki/High_jump

I wonder if the world record would be higher if they were allowed to jump with a different style using both legs. It looks like the current world record stands at 2.45m, set in 1993.

 

[Shooting Star]

Hi,

I was playing basketball the other day and I noticed something that puzzled me. Why is it that when I jump off of one leg I jump just as high as when I jump off of two? Shouldn't I be exerting 2x the force when jumping off of two legs? And if I am exerting 2x the force, shouldn't I be jumping much higher? Any response on this question is greatly appreciated...

I am not very sure that the result reported in the OP is completely correct. More experiments under controlled conditions and with more precise measurements may be required to study this phenomenon.

Two legs, acting like two springs, at maximum compression, should release double the energy than one leg whose "spring" (the collection of muscles) is compressed to the same maximum degree.

Assuming that roughly the result is true, here's a possible explanation, where one subtle point about human body MAY come into play. (I’ve not analysed it too far.) The body during physical exertion has only a certain amount of energy reserve to give per unit time. So, whether you are using one or two legs may not matter, since the height you jump up to depends on the total energy output. (Of course, during crisis, the output is far more than under normal conditions.) The one leg, in this case, is far more compressed than each of the legs when two are being used. The body does this unconsciously, and you may more or less jump up to the same height. It's obvious that the one leg will be under more strain.

So far, I have assumed standing jumps, where you bend your legs, crouch down, and then jump up. The argument holds good where you are bouncing off a previous jump.

And let me just mention here, that by throwing up your arms, you do not impart any net momentum to your body, much as you can’t lift yourself up by your bootstraps. If anything, you stretch out your arms, thus increasing your reach slightly.
.

 

[idea2000]

Hi,

I actually used to do high jump and long jump in track and field when I was still in school, incidentally. I do notice a bit of an increase in height when I jump with both legs, but it's only on the order of a couple of inches, not what you would expect if you were actually using 2x the force.

I do notice, however, that when I really need an extra burst of energy, I do go higher sometimes while I am playing basketball and fighting for a high rebound. I suspect that the answer might have something to do with (as star pointed out) our body physiology or (as berkeman pointed out) the mechanics of our movement or the mechanical structure of our body.