Why we jump with the same initial speed on 2 different planets?

[jaumzaum]

In every single question asking about the maximum height you get from jumping in 2 different planets they consider that the speed you leave the ground is constant. Why is that?

Speed would be constant if impulse were constant. Impulse would be constant if both force and time were constants. But I cannot explain why this would be true. Force exerted on ground is equal to the normal force (third Newton Law), and the normal force is equal to the weight + net force that will actually produce an acceleration. The first one is dependent on gravity. Also, it is not that clear why my jump movement (moving my bones and joints) would take the same time in 2 different planets.

 

[anorlunda]

In every single question asking about the maximum height you get from jumping in 2 different planets they consider that the speed you leave the ground is constant.

Please give us links to where you saw that. Your sentence implies that there are several.

 

[Nugatory]

In every single question asking about the maximum height you get from jumping in 2 different planets they consider that the speed you leave the ground is constant. Why is that?

“Every single” might be an overstatement but yes, there are a lot of descriptions out there that say that. Most of them are assuming an idealized launch mechanism that transfers a fixed amount of momentum and kinetic energy to the launched object; naturally this leads to the same launch velocity on all planets. Many of these fail to state this assumption explicitly.

You are of course correct that this idealized launch mechanism is a poor description of a jumping human.

 

[PeroK]

And if you are on the Moon you will have your space suit on. They don't take that into account either.

 

[A.T.]

In every single question asking about the maximum height you get from jumping in 2 different planets they consider that the speed you leave the ground is constant. Why is that?

Because estimating the lift-off speed for a different gravity is not trivial, as it involves human biomechanics, which is optimized for Earth's gravity.

There is a lengthy thread on this here:
https://www.physicsforums.com/threa...ump-21-times-higher-than-on-the-earth.774140/

Here is what I proposed back then to get more realistic data on this:

An experimental way to estimate it could be an inclined rowing machine, such that the person pushes off with legs against 1/6 of its weight (instead of the string). From this you could get the take-off speed at 1/6 g.

 

[Dale]

In every single question asking about the maximum height you get from jumping in 2 different planets they consider that the speed you leave the ground is constant. Why is that?

Because it makes the problem solve-able by physics students.

Seriously, this should not be taken as a claim of fact. It is a simplification used for homework purposes.

 

[Vanadium 50]

Next you're going to say there's no such thing as stretchless ropes or frictionless planes.

 

[Nugatory]

Next you're going to say there's no such thing as stretchless ropes

Only a piker would stop at stretchless ropes when there's an entire universe of problems that are simplified by assuming that ropes are also massless.

And seriously, kidding aside, @jaumzaum you may reasonably infer from this flood of tongue-in-cheek responses that you are not the only person who is sometimes a bit annoyed by failure to state assumptions. How hard would it be to replace the jumping humans with spring guns or cannons (both of which provide an excellent approximation of the ideal launching device)?

 

[Dale]

How hard would it be to replace the jumping humans with spring guns or cannons (both of which provide an excellent approximation of the ideal launching device)?

Indeed, most “human body” physics problems that are confusing are very simple when replaced with springs. Typically without losing any of the pedagogy.

 

[jrmichler]

Indeed, most “human body” physics problems that are confusing are very simple when replaced with springs. Typically without losing any of the pedagogy.

Only if we can assume that the springs are massless.

 

[Nugatory]

Only if we can assume that the springs are massless.

It gets appreciably harder when we don't assume that the springs are massless (likely we have to integrate a mass density across a length of the spring, at which point we retreat to the next level of wimping out and assume a uniform density to simplify the integral)... but it's still a whole lot easier than any complete and realistic treatment of this glob of non-uniform non-rigid non-linear randomly assembled bioslop that we call a human body.

 

[gmax137]

Next you're going to say there's no such thing as stretchless ropes or frictionless planes.

I get those, as well as massless pulleys and point sources, down at the Ideal Hardware Store.

 

[A.T.]

I get those, as well as massless pulleys and point sources, down at the Ideal Hardware Store.

This one?
https://lockhaven.edu/~dsimanek/ideal/ideal.htm

 

[sophiecentaur]

Real ropes, pulleys and springs are still way more easy to analyse than a jumping human. But my advice is to start with the really ideal situation and gradually add in practical details.

You have to acknowledge that we have evolved under Earth conditions (as @A.T. implies) Our legs and muscles (and the way they are attached) are well suited to our situation. On another planet, we would weigh a different amount but our mass would be the same. You could say that we would be working in the wrong gear on another planet. We would assume that we use the same muscle mass on each planet.

Higher gravity would require a 'lower gear' with shorter legs and muscle attachments further out from the joint. Under lower gravity our legs would not be able to travel fast enough to make use of the muscle strength; it would be like cycling downhill in a normal gear when your legs can't catch up with the pedals. That could be compensated for a bit by using some fancy levers to lengthen the 'levers' of our legs. That could allow your muscles to work nearer optimally.
As has been mentioned above, there are add ons or helpers to provide a real human subject with similar gravitational environment as would be found on another planet. This is bound to have been tried and you could do a fruitful search for work that's been done already.

 

[jaumzaum]

Thanks guys! Specially @Nugatory @sophiecentaur @A.T. and @Dale

Could you help me to figure out when we could make those assumptions? I would like to create a similar problem, but I want to do it with the right assumptions and the right gear to make the problem solvable and flawless.

Let's analyse the problem to see what a constant initial velocity implies:
1) First, I will consider that when I jump I bend my knee and lower my center of mass (CM) h centimetres, and this will be constant in both planets.
2) I will also assume that I will leave the ground when my legs are completely straight (is this assumption fair and correct?).
3) I will assume that the acceleration of my CM upwards during the knee-unbending movement is constant (I know this isn't true but I don't think it will affect the problem much)
4) I will also assume that the force I exert on the ground will be constant in different planets. This is, in my opinion, the worst assumption, as @sophiecentaur said we need to consider the biological factors. I will have the same muscle mass here and on the Moon, but I was designed to live here. My muscles won't work properly there. Support muscles that exist only to make me stand will be unconfigured. Some of them will be more contracted, others more relaxed. Some will help the jump, others will make it more difficult. So I cannot say the force I will do on the ground will be constant, do you agree? But let's consider this for oversimplification

Suppose my feet reach a height H from the ground and the force I exert on the ground is N, the upward acceleration of the CM during the knee-unbending movement is a and the velocity that I leave the ground is v:
$$N-mg=ma$$
$$V^2=2ah$$
$$V^2=2gH$$
Where we get, when we suppose N constant:
$$g(H+h) const. $$

So the assumption that the velocity from which we leave the ground is the same in both planets (analogous to say gH is contant) is only valid if wee consider h<<H, which is of course not valid.

Do you agree with those assumptions?

No for the real world. Which ideal device would have the same initial velocity? I was thinking about a gun. Are there others? Why would they provide a constant initial velocity in both planets?

Thank you!

 

[Dale]

Could you help me to figure out when we could make those assumptions?

Any time you want the calculations to be easy. Seriously, you are overthinking this. This is not a well justified approximation, it is a brazen simplification.

 

[A.T.]

Let's analyse the problem to see what a constant initial velocity implies:
...
4) I will also assume that the force I exert on the ground will be constant in different planets.

Same force will not give you the same lift-off velocity. Seems like you are trying to combine incompatible assumptions.

 

[PeroK]

Could you help me to figure out when we could make those assumptions? I would like to create a similar problem, but I want to do it with the right assumptions and the right gear to make the problem solvable and flawless.

The fact is that unless you have some very sophisticated biomechanics, you would have to measure the speed at which a human being leaves the ground on different planets. This might give you a simple formula for $v$ in terms of $g$.

Physics is about real data as well as theoretical calculations.

 

[haruspex]

What nobody seems to have pointed out is that take-off speed and height jumped need to be defined.

I don't jump from a standing position; I crouch down so that my legs can apply force over some distance. This means that by the time my feet leave the ground I have already done some work against gravity. My maximum speed will have occurred slightly earlier.
The work that I do relates to the maximum vertical rise of my mass centre, not of my feet or head,

So if we define height jumped as the mass centre rise, and define take-off speed as the speed I would have reached in the absence of gravity, it becomes a lot more reasonable to assume the height reached is inversely proportional to the gravitational field strength.
Even then, this assumes that legs can do the same work during extension over a range of gravitational field strengths, which is probably false. Muscles can do more work when meeting the optimum level of resistance.