# Quick question on work and energy

ElementsnStuff
I thought of this recently, and want to know if there's something I'm missing.

So, say a very fragile object decelerates to a stop from a given velocity. For example, a free-falling object hitting the ground.

But, all the kinetic energy is absorbed through use of some clever mechanics (assume magic for this part).

If no energy was transmitted to the object, and (therefore) no work was done on it, would the fragile object still be harmed?

Mentor
Welcome to PF!

If a fairy could play baseball, what would her batting average be? I'm sorry, but if the scenario is "magic", there is no possible useful answer that science can provide. In Star Trek, they explain away the effects of absurdly high acclerations that would turn people into thin puddles of goo with the words "inertial dampers".

Can you rephrase it into something a little more physically realistic? Maybe a shock absorber or an airbag to stop the fall...?

ElementsnStuff
Sure, I guess. It has absurdly efficient shock-absorbing gear that absorbs all the energy.
Honestly, this is more of a conceptual question, so I didn't feel like an explanation was necessary.

Mentor
Well, an airbag is very good at evenly absorbing a lot of energy from a falling object without damaging it.

Mentor
2021 Award
If no energy was transmitted to the object, and (therefore) no work was done on it, would the fragile object still be harmed?
Energy per set isn't what harms fragile objects. Stress is what harms them.

all the kinetic energy is absorbed
If all the object's KE is absorbed by something else than the object, then the object obviously won't get damaged.

and (therefore) no work was done on it,
Negative work is still being done on the object, to extract energy from it.

ElementsnStuff
Extract energy from it? I don't quite understand...

jerromyjon
An egg, falling at terminal velocity, has kinetic energy. If it hits the ground where does the energy go? If it hit an air bag and didn't break?

Mentor
2021 Award
Extract energy from it? I don't quite understand...
When it is in motion, it has KE > 0. When it is stopped, it has KE = 0. To go from one to the other requires energy to be removed.

Extract energy from it? I don't quite understand...
The object has initially some KE. After the object stopped it has no KE. The KE must have been removed by doing negative work on the object.

The only question here is where the extracted energy goes. If it goes into deformation energy of the object, it will break. If can be be transferred away from the object it will survive.

ElementsnStuff
Ah. So then, could this be extended to a human as well? Say, if an airbag was surreptitiously strapped to someone's feet and they were shoved off a cliff (for science, of course), and all their kinetic energy was absorbed, they'd be fine?

jerromyjon
The air bag is much larger than a person in order to gently slow them down, so it is usually the large target on the ground with a smaller "sweet spot" in the middle where it is most effective.

Say, if an airbag was surreptitiously strapped to someone's feet and they were shoved off a cliff (for science, of course), and all their kinetic energy was absorbed, they'd be fine?
Depends on the size of the airbag. In reality you will never absorb all the KE, but you can reduce the amount that goes into the body. A good way to protect a human from impact damage is to put him into a capsule filled with water.

Homework Helper
Gold Member
Ah. So then, could this be extended to a human as well? Say, if an airbag was surreptitiously strapped to someone's feet and they were shoved off a cliff (for science, of course), and all their kinetic energy was absorbed, they'd be fine?

Not necessarily... As AT said... it depends on the size of the airbag.

If you used a small spherical airbag say 2ft in diameter the stopping distance would have to be less than 2ft. In other words after jumping off they would get faster and faster until the bottom of the airbag hit the ground. At that point they would going fast and only be 2ft off the ground. Then they would have to decelerate from a high speed to zero in less than the remaining 2 feet. The rate of deceleration ("g force" if you prefer) would have to be very high - like a car stopping from perhaps 100mph in less that 2 feet! Their internal organs might squish against the inside of there chest!

If you use a much larger air bag the stopping distance could be longer and the g forces lower. They are more likely to survive.

Stunt men sometimes leap off buildings onto air bags placed on the ground. These are usually quite deep so that the "stopping distance" isn't too short. Even so they still experience quite high g forces which is why they try and land flat on their back...

jerromyjon
That video is 3 minutes of exponentially increasing adrenaline.

jerromyjon
a capsule filled with water
Essentially you'd need as much water to travel through as if you fell and hit a pool but without the *smack* of transitioning from air to liquid? Wouldn't that be capable of a greater rebound back like a shockwave?

Essentially you'd need as much water to travel through as if you fell and hit a pool
No. You would barley move through the fluid, if you adjust its density to match the density of the body. The capsule would have to be just big enough for the human to fit in.

jerromyjon
That just doesn't sound right to me. Say you have centimeters of water in front of and all around you and you hit the ground and come to an almost complete stop (barely move as you put it) instantly while "protecting the human" who experiences very high g's in this sudden stop.

billy_joule
That just doesn't sound right to me.
Consider a plastic bag filled with a liquid floating in a capsule filled with the same liquid. Now the capsule undergoes high acceleration, but doesn't break or deform significantly. Why should the liquid in the bag move relative to the rest of the liquid?

The human body is obviously not just a bag of liquid, so high pressure gradients / shock waves propagating though it can cause internal damage too. But the body will not suddenly start moving fast though an accelerated liquid of same density to hit the capsule wall.

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ElementsnStuff
So, if rapid deceleration harms the body upon impact, is there any way to circumvent this? I had another thought where the person would be standing on some mechanical contraption that converted the downward direction of deceleration into a rotation - rather like an odd cross between a hamster wheel and a unicycle. This would then be submerged in some very viscous fluid. As the person landed, the impact of hitting the ground, while not decelerating them initially, would cause them to begin rotating about the center axis of this device, and the fluid would absorb energy and acceleration through friction. This would (hopefully) cause the human to not experience any rapid deceleration, and absorb all the kinetic energy as well - but is something like this even possible? I feel like if it was, it would've been done before...

As to the previous posts regarding the bag of liquid, could this be practically utilized as a sort of 'covering'? That is, could a thick shell be made where the body is submerged in liquid, and this would absorb all the acceleration?

Thanks for the responses so far, I'm learning a lot.

Mentor
An olympic ski jump does that. Their run starts around 140m off the ground and the launch point 85m. They land on a slope 25m above the ground. If not for the slope, the 60m fall would probably kill them. Instead, the slope lightly catches them, then curves gently to covert the downward motion to horizontal motion. The key is having a gentle enough - and therefore wide enough - curve to handle the deceleration standing up.

I had another thought where the person would be standing on some mechanical contraption that converted the downward direction of deceleration into a rotation - rather like an odd cross between a hamster wheel and a unicycle.
Yes, using a long curved (circular) braking path might be more place saving than a long linear breaking path. But it's the same principle: you use a long duration to slow down, thus reducing the force.

As to the previous posts regarding the bag of liquid, could this be practically utilized as a sort of 'covering'? That is, could a thick shell be made where the body is submerged in liquid, and this would absorb all the acceleration?
It doesn't absorb the acceleration. The body does undergo s huge acceleration, but the force is applied such that the acceleration is relatively uniform across the body, keeping the internal stresses relatively low. Short of science fiction stuff (like the "inertia dampers" from Star Trek), buoyant force seems like the best option for applying a huge acceleration to the body.

Ben Johnson
Where is the energy transferred once the viscous liquid absorbs it?

Could transfer the energy as exhaust after using the rotational motion to spin a gyroscope powering a generator...

The energy needs to be transferred from the system with the human to the system without the human.

Gold Member
I am trying to come to terms with the idea of converting linear momentum to angular momentum and I can't quite see how it would help. Either way, it's a matter of dissipating Kinetic Energy. Would a rotation make this any easier?
You have to slow down all of your body (inside bits too) at nearly the same rate. A G suit will protect you from the effects of blood sloshing down to your feet and away from your brain as you pull out of a dive because it encases your body tightly restricting the ability to expand and keeping blood up in your head. A rigid fluid sac would achieve the same thing but it would not stop more dense organs from sinking down and damaging tissues.
It really would depend upon what sort of spec you actually needed and how large your protective 'egg' could be. The longer time you can spread the effects of the acceleration, the less force is involved. (The crumple zone in a car does it for relatively mild impacts.)

Either way, it's a matter of dissipating Kinetic Energy. Would a rotation make this any easier?
If you have limted space, yes.

Homework Helper
If you have limted space, yes.

The vertical distance covered bringing a falling object to a stop with a uniform upward vertical acceleration will obviously be lower than the vertical distance covered using a profile that is limited to the same maximum acceleration magnitude but which involves any non-zero horizontal acceleration.

The horizontal distance covered bringing such an object to a stop will be zero using a uniform upward vertical acceleration (assuming the object started with zero horizontal velocity).

So... what sort of space limitations are you considering?

As to the previous posts regarding the bag of liquid, could this be practically utilized as a sort of 'covering'? That is, could a thick shell be made where the body is submerged in liquid, and this would absorb all the acceleration?
James Essig posted an interesting article in another thread:

When floating in a liquid, and using liquid ventilation mice can stand 3800g for 15min "without any physical impairment" (no loss of
consciousness etc.).

ElementsnStuff
James Essig posted an interesting article in another thread:

When floating in a liquid, and using liquid ventilation mice can stand 3800g for 15min "without any physical impairment" (no loss of
consciousness etc.).

Very interesting. 3800g would indicate that with half an inch of deceleration distance, the maximum height one could fall with this setup would then be about 48 meters - not too shabby.

I wonder what a shear thinning fluid would do here? Not out of any application to the subject at hand, just out of curiosity. Would you be able to develop a system where the solid material is placed as a fully bodysuit, and upon landing this shifts to a liquid of appropriate density?

Very interesting. 3800g would indicate that with half an inch of deceleration distance, the maximum height one could fall with this setup would then be about 48 meters - not too shabby.
Keep in mind that the acceleration for these mice was probably increased relatively slowly. During impacts you have a short peak, which might produce other adverse effects, like shock waves propagating through the liquid, and the body.

ElementsnStuff
Keep in mind that the acceleration for these mice was probably increased relatively slowly. During impacts you have a short peak, which might produce other adverse effects, like shock waves propagating through the liquid, and the body.

Alright. So, how does one avoid the propagation of shock waves through the body? Literature search hasn't done much for me, or maybe my Google-fu has dropped considerably since the last time I researched this.

If I'm reading this thread right, so far there are established methods to limit the effects of deceleration, stress, and kinetic energy on a body. Therefore, all that seems to be left are shock waves...

If I'm reading this thread right, so far there are established methods to limit the effects of deceleration, stress, and kinetic energy on a body. Therefore, all that seems to be left are shock waves...
That's a bit backwards. The method limits the stresses themselves (not the effects of stresses) during high acceleration (but low jerk). Shock waves (due to high jerk) are one way to dissipate the kinetic energy of the object. The method is usually to dissipate the kinetic energy by destroying some softer crumple zone, to protect the important parts in a harder shell.

ElementsnStuff
Back to the question of deceleration: My goal here is to make the vertical distance of deceleration as small as possible without harming the body. To that end, would it be possible to do the following:

-Attach a bunch of tiny, hollow cylindrical 'wheels' to the bottom of the system. Through these are connected a bunch of axial rods which are rigidly attached to the system, and the whole setup is encased in a semi-viscous fluid. The rods are, through some means, made to stay on the side of the tube until the moment of impact. Upon impact, the rods begin rapidly rotating around the inside of the tubes, converting the deceleration into rotational force and slowing down via means of the viscous fluid until they are once again at rest.

Is this a viable means of safely removing deceleration from a system? I'm mainly just trying to convert that idea about the ski slopes from earlier into something mechanical. If this isn't a good idea, does anyone have a better one?

Gold Member
I thought of this recently, and want to know if there's something I'm missing.

So, say a very fragile object decelerates to a stop from a given velocity. For example, a free-falling object hitting the ground.

But, all the kinetic energy is absorbed through use of some clever mechanics (assume magic for this part).

If no energy was transmitted to the object, and (therefore) no work was done on it, would the fragile object still be harmed?
The "magic" gets that energy. If the magic is sand and falling object is ball, then energy kinetic energy turns to thermal energy of ball and sand. Work is done during the impact.