# Physics of the Frog Jump

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• makamo66
I think the simplest explanation is that kinetic energy (K) increases as potential energy (U) decreases because of the conservation of mechanical energy: E = K + U.In summary, the frog jump is an exercise where you jump forward as much as you can with both legs. You swing your arms forward to gain momentum. This increases your moment of inertia and helps you jump higher.f

#### makamo66

I'm trying to understand sports physics and I have a question about an exercise we do at my taekwondo studio. For the line drills, we do something called the frog jump where you jump forward as much as you can with both legs. Everyone swings their arms forward to gain momentum. What does this mean physically? Are we shifting the angular momentum to the arms? Are we increasing our moment of inertia? Is the change of the center of mass relevant?

An interesting question reminds me of the Mark Twain story The Celebrated Frog of Calvaras County

https://twain.lib.virginia.edu/projects/price/frog.htm

A related activity is the long jump whose physics is similar

Here's a study on jumping and swinging yout arms

https://iopscience.iop.org/article/10.1088/1742-6596/2071/1/012018/meta

and this one on vertical jumps

https://www.topendsports.com/testing/vertical-jump-physics.htm

pinball1970 and PeroK
Are we shifting the angular momentum to the arms? Are we increasing our moment of inertia? Is the change of the center of mass relevant?

You are gaining C of Mass momentum in the desired direction before you need to use your legs. Every little bit helps. Also it makes you tip forward so you start from a little further forward. Every little bit helps

jbriggs444
You are also buying a tiny bit of time for the muscles to ramp up from zero force to maximum force.

hutchphd
I appreciate all of the links. I read all of them. I also ordered the book by JG Hay from the bibliography of the googles site link from Thriftbooks for about \$5. I still have a question though. If you print out the google site so that you see page numbers, there are comments on page 4-5 that I don't understand. The paper says that the athlete during the transition from run up to take off begins to lower his center of mass. As a result of lowering the COM, the take off height is decreased. I thought the idea was to increase the take off height so that one jumps further and not decrease it. What am I misunderstanding?

The runner is moving in a parabola, so I guess the jump will be longer the less tall it is.

What I understood from the links you gave me is that the long jump would represent a rotation and the moment of inertia (MOI) would become larger when the arms are extended while jumping. Since angular momentum is conserved, the angular velocity would decrease and the larger MOI would prevent too much rotation. This however doesn't make sense to me because I don't see how the jump can be considered to be rotational.

What I understood from the links you gave me is that the long jump would represent a rotation and the moment of inertia (MOI) would become larger when the arms are extended while jumping. Since angular momentum is conserved, the angular velocity would decrease and the larger MOI would prevent too much rotation. This however doesn't make sense to me because I don't see how the jump can be considered to be rotational.
This is intuitive rather than analytic.
Jumping from a stop involves gaining purchase from the floor.
Use of the arms rather than leaving them dangling at the side takes part in the forward movement. A contribution.

As a result of lowering the COM, the take off height is decreased. I thought the idea was to increase the take off height so that one jumps further and not decrease it. What am I misunderstanding?
CAVEAT: I have not looked at the literature.
The question here is one of physiology. I presume the takoff height is dictated only by the length of your legs after you straighten up. If you crouch down the legs will provide force (presumed invariate) over a longer distance. Bigger energy.

As a result of lowering the COM, the take off height is decreased. I thought the idea was to increase the take off height so that one jumps further and not decrease it. What am I misunderstanding?
I seem to remember reading that, for long jump, you need your CM to be as high as possible but, for high jump, you need your CM to be as low as possible. An over simplification, perhaps but.

I guess it's because the length you can travel will depend on the time you are 'in the air' but to jump high, you will have your CM actually below the height of the bar. Hence the body curve in the Fosbury Flop and the pole vault.

I think the simplest explanation is that kinetic energy (K) increases as potential energy (U) decreases because of the conservation of mechanical energy: E = K + U.
U = mgh_com where h_com is the height above the ground of the jumper's center of mass.

The runner is moving in a parabola, so I guess the jump will be longer the less tall it is.
It depends on the proportions of the individual body. Power / Weight (we mean Mass, really) ratio is a factor and also the mechanical advantage of the leg (lever) bones etc. Any answer to the OP must really relate to one particular jumper.
Only whilst the person is actually not in contact with the ground can you say that the path of the Centre of Mass is a parabola. Initiating the jump will involve optimising the vertical and horizontal velocities achieved (as with most ballistics problems).
Everyone swings their arms forward to gain momentum.
Your arms are given both vertical and horizontal momentum at the start. Afair you use the arms to 'pull yourself up' as you're in free fall. I'd say they start off moving upwards and forward and, on impact with the floor, they are moving down and backwards. I don't know if the exercise has an actual name but frog jump performance can be improved by carrying an appropriate size of kettle bells to increase the effective mass of the arms. With that method, one is seriously aware of the feeling of pulling yourself towards the kettle bells - they're like free ballistic energy which was stored before you took off..

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