How much force is required to jump?

[pleb22]

Hi there,

I'm interested in the force required to jump. It's been a decade since physics, my old copy of Serway is 1,000 miles away, and I can't remember enough about solving the problem to put proper keywords into a Google search (yeah, it's pathetic).

I remember enough about Newtonian kinematics and projectile motion to solve or derive for initial velocity/time of flight/etc, but I can't remember how to relate initial velocity to force. Is there an instantaneous acceleration at the moment of lift-off while jumping? Can I use the F=MA equation, or do I need to look at kinetic energy?

Ultimately, I'd like to know how jump-height changes with body strength (if I were twice as strong, how much higher could I jump?). Would anyone be willing to walk me through the process of solving this, please?

Thanks in advance,
Plebe

 

[pleb22]

Anyone?

 

[HallsofIvy]

We keep getting this kind of question! There is no way to calculate the force required to jump a given height. It is energy that determines the height, not the force. Taking your original height as the "0" for potential energy, at height "h" you have gained potential energy mgh where m is you mass and g is acceleration due to gravity- about 9.81 m/s^2 at sea level.

But "energy= force times distance" and the distance there is the distance you rose while still in contact with earth. That is, if you squat down and the leap upward, the distance will be greater and so you can produce the same energy (and so jump to the same height) with less force during the jump than if you try to jump from a standing position.

 

[K^2]

You can make a rough estimate, though. Your body travels about half of a meter when you apply force for the jump. So if you want to jump a meter up, you'll need to apply 3x your own weight (1x just to support body, plus 2x because it is 2x the height).

 

[rcgldr]

I recall that a gymnast doing a standing back flip reaches a peak acceleration of around 5 g's during a jump.

 

[K^2]

A peak, maybe. But I doubt that the average is anywhere close. They'd jump a lot higher otherwise.

 

[pleb22]

Thank you, all, for the replies. I did not realize that it was a frequently asked question, as my searches did not turn up answers that seemed in synch with my question.

The idea for approximating the force seems reasonable - thank you.

With regard to the statement that I need to be looking at energy instead of force, would it be possible to instead frame the question as follows? "Upon jumping as high as I possibly could, I achieved a height of one meter. Is the potential energy at my peak height equal to the energy required for me to jump one meter? Is this expressed as mgh? If I weigh 1 kilo, is it true that it requires 9.8 Joules to jump one meter?

Finally, if we pretend that the acting forces are constant (ignoring air resistance, stretchy tendons, etc), is it true that my highest jump will scale linearly with my strength?

Thanks for your consideration,
Pleb