Physics of Falling

[Business Scrub]

Hey there everyone. It's very likely that my question could be answered in the first post, but I can't find a good answer on the interwebz.

So, I'm looking to calculate the force of a falling object (specifically a creature of basically human structure, so lets call it a human. It's for a story, I promise I'm not dropping people out of planes), to see if it really is enough to break stone or concrete like in the movies when the superhero falls from the sky.

The site I have found say F=m*a. Well, that seems simple enough. Mass = 120 lbs. (54,400 g), and acceleration should be 9.8 m/s/s. However, that confuses me for two reasons:
An object falling 80 mph (accelerating at 9.8 m/s/s) seems like it would have way more force behind it than the same object falling at 5 mph (accelerating at the same rate.) Can someone please explain this?

Secondly, the object apparently hit terminal velocity at around 175 mph, (78.2 m/s). Well, if it's not accelerating, its acceleration = 0, yes? So by the formula above it would have no force behind it, and that's definitely not true.

Awesome bonus (full) question, since I have no idea how I would begin to figure this out. (If you do I have an immense amount of respect for you):

The 120 lb. person described above is ejected from a shuttle 10000 km above sea level at 2 mph (.89 m/s), directly towards earth. How long would it take them to hit ground at sea level (terminal velocity for this person is 78.2 m/s)?

Assuming the person lands in Yale University (41.3163244, -72.9223431) or very close to there, where did they leave the shuttle? (Anything nearly impossible to calculate, I'm guessing jet streams and the like, can be ignored.)

Finally, the person falls into a layer of concrete an inch thick (think hitting the lip of a fountain). Will the person break through it? If so, when they hit the stone ground 1.5 feet (.46 m) below that, will they bounce any significant amount (more than a foot)? And if so, how many of these bounces?


Thanks to everyone for considering it. I'm also very curious into the technical bits behind this (particularly the full question), so I'd really appreciate if someone walked through your reasoning behind the explanation.
(And in case you're concerned, don't worry: our unfortunate subject survives, based on her alien ability to regrow. :smallsmile:)

[Sabeki]

I don't think that the forums are a good way to solve hw problems.

[AsteriskAmp]

Hey there everyone. It's very likely that my question could be answered in the first post, but I can't find a good answer on the interwebz.

So, I'm looking to calculate the force of a falling object (specifically a creature of basically human structure, so lets call it a human. It's for a story, I promise I'm not dropping people out of planes), to see if it really is enough to break stone or concrete like in the movies when the superhero falls from the sky.

The site I have found say F=m*a. Well, that seems simple enough. Mass = 120 lbs. (54,400 g), and acceleration should be 9.8 m/s/s. However, that confuses me for two reasons:
An object falling 80 mph (accelerating at 9.8 m/s/s) seems like it would have way more force behind it than the same object falling at 5 mph (accelerating at the same rate.) Can someone please explain this?It's related to a concept called impulsive forces, which account for speed rather than acceleration at the moment of a collision. They are linked to amount of momentum or inertia which is mass*velocity and how it changes on the moment of impact.

The force that two colliding bodies exert on one another acts only for a short time, giving a brief but strong push. This force is called an impulsive force. During the collision, the impulsive force is much stronger than any other forces that may be present; consequently, the impulsive force produces a large change in the motion while the other forces produce only small and insignificant changes. For example, during the ceilling crash, the only important force is the push of the person on the ceilling; the effects produced by gravity, the normal from the roof and by the viscous force of the air during the collision are insignificant.

To calculate the force at the moment of impact you require:
Duration of impact, change in speed before and after the crash through and mass of the projectile. The bigger the speed change, or the smaller the impact duration the bigger the force.

Secondly, the object apparently hit terminal velocity at around 175 mph, (78.2 m/s). Well, if it's not accelerating, its acceleration = 0, yes? So by the formula above it would have no force behind it, and that's definitely not true.
There IS a force, it's just counterbalanced by viscosity's force in the opposite direction. And yes, for purposes during the fall it's net force would be 0, but at the moment of impact refer to upper paragraph.

Awesome bonus (full) question, since I have no idea how I would begin to figure this out. (If you do I have an immense amount of respect for you):

The 120 lb. person described above is ejected from a shuttle 10000 km above sea level at 2 mph (.89 m/s), directly towards earth. How long would it take them to hit ground at sea level (terminal velocity for this person is 78.2 m/s)?

Assuming the person lands in Yale University (41.3163244, -72.9223431) or very close to there, where did they leave the shuttle? (Anything nearly impossible to calculate, I'm guessing jet streams and the like, can be ignored.)

Finally, the person falls into a layer of concrete an inch thick (think hitting the lip of a fountain). Will the person break through it? If so, when they hit the stone ground 1.5 feet (.46 m) below that, will they bounce any significant amount (more than a foot)? And if so, how many of these bounces?


Thanks to everyone for considering it. I'm also very curious into the technical bits behind this (particularly the full question), so I'd really appreciate if someone walked through your reasoning behind the explanation.
(And in case you're concerned, don't worry: our unfortunate subject survives, based on her alien ability to regrow. :smallsmile:)EDIT: At that point you are on the limit of what we consider Earth. It's deep into the Exosphere...

You'll need gravitation law rather than free fall for falling from orbit due to changes in gravity due to height. On top of that terminal velocity also varies according to height. If you ignore both then it's a simple free fall problem though you just limit the speed at the terminal velocity.

Odds are you'll need material resistance and thickness and elasticity to determine if it breaks through or bounces. Humans are not elastic enough from my knowledge due to all those annoying soft parts and the thick parts being made to resist impact, so it's unlikely any person no matter weight wouldn't be able to bounce any distance, though with high enough speeds and some bouncy material (definitely not concrete) you might get said bounce to be significant enough.

As for breaking through concrete though... I severely doubt it due to it's resistance to impact, especially when said something is much much less resistant than it.

[Randomguy]

So, I'm looking to calculate the force of a falling object (specifically a creature of basically human structure, so lets call it a human. It's for a story, I promise I'm not dropping people out of planes), to see if it really is enough to break stone or concrete like in the movies when the superhero falls from the sky.

The site I have found say F=m*a. Well, that seems simple enough. Mass = 120 lbs. (54,400 g), and acceleration should be 9.8 m/s/s. However, that confuses me for two reasons:
An object falling 80 mph (accelerating at 9.8 m/s/s) seems like it would have way more force behind it than the same object falling at 5 mph (accelerating at the same rate.) Can someone please explain this?

Secondly, the object apparently hit terminal velocity at around 175 mph, (78.2 m/s). Well, if it's not accelerating, its acceleration = 0, yes? So by the formula above it would have no force behind it, and that's definitely not true.

I think you're getting "force acting on the object" and "the force that the falling object applies onto the ground when it hits the ground" (which is the same as the force that the ground applies on the falling object) mixed up. All of these numbers you're using have to do with the forces of gravity and friction that are acting on the object, so yes, something that's falling at terminal velocity is being acted upon by a net force of 0 (but the Force of gravity on your 120 pound object is still 533.12 N, just like it was when it started falling. It's just that the force of air friction acting on your object is also 533.12N in the opposite direction, so they cancel each other out).

The force that the ground applies to your object is also calculated as F = ma, but a isn't the acceleration at which you are falling, it's the acceleration at which you're stopping.
To calculate that, use a = v / t, where v = speed at which you hit the ground and t = time it takes you to stop. The longer it takes you to stop, the lower your acceleration and the lower your force of impact. This is why falling on water or something soft, which takes a long time to slow you to a stop, hurts less than falling on concrete, where you decelerate to a stop very quickly.

It's not the force of the fall that kills you, it's the force of the sudden stop at the bottom.

[Business Scrub]

Ok, that shines a lot of light on this. Thanks araveugnitsuga and RandomGuy! :smallsmile:


This is why falling on water or something soft, which takes a long time to slow you to a stop, hurts less than falling on concrete, where you decelerate to a stop very quickly.

It's not the force of the fall that kills you, it's the force of the sudden stop at the bottom.

And now I'm remembering a video in physics where someone threw an egg at at a wall and the egg smashed, then threw another one at a sheet and the egg didn't smash. I'm guessing the same idea is at work here? Also is there some index that looks up something's 'give'?

Sabeki: I don't really know how you got the wrong impression, but I'm just curious about this. So I'd politely ask you to stop prejudging things, especially if you have nothing to positively contribute.

[Sabeki]

Sorry about that. It was pretty rude of me to do so without asking first.

[AsteriskAmp]

And now I'm remembering a video in physics where someone threw an egg at at a wall and the egg smashed, then threw another one at a sheet and the egg didn't smash. I'm guessing the same idea is at work here? Also is there some index that looks up something's 'give'?Similar principle to the use of paper containers and straws to cushion throwing an egg from a second or higher story. If you manage to prolong the impact's duration it will mean the stopping is less violent.

Similar to braking suddenly or gradually or against a wall.

Sabeki: I don't really know how you got the wrong impression, but I'm just curious about this. So I'd politely ask you to stop prejudging things, especially if you have nothing to positively contribute.Whilst he may be wrong in terms of it being a homework question, and the playground is a certainly viable place to ask this sort of questions (since I'm aware there are physicists amongst us and a good deal of Engineering/Science people), there is a chance a more specialised forum like Physics Forum would be able to provide more substantial answers and probably actual numerical results since it's specialised in this sort of questions.

[Business Scrub]

Sorry about that. It was pretty rude of me to do so without asking first.

No worries, its fine. :smallsmile:

@^: That's certainly true, I've just found people on those sites to be either unhelpful (This is your answer: __ ), or not willing to explain more basic concepts.

[Gray Mage]

However, that confuses me for two reasons:
An object falling 80 mph (accelerating at 9.8 m/s/s) seems like it would have way more force behind it than the same object falling at 5 mph (accelerating at the same rate.) Can someone please explain this?


Yes. The force is the same, but you might be thinking about (kinetic) energy [mv²/2], in which case, yes, the one at 80 mph has way more then the one at 5 mph.



The 120 lb. person described above is ejected from a shuttle 10000 km above sea level at 2 mph (.89 m/s), directly towards earth. How long would it take them to hit ground at sea level (terminal velocity for this person is 78.2 m/s)?


Ok, I'll assume that the gravity is constant (a very wrong assumption, but for a quick calculation it'll have to do. Maybe later I'll make one with gravity as a function of height). So it's a free fall problem.

First, we calculate how long would it take to reach terminal velocity.

V = g*t1.

Assuming g = 9.8 m/s².

t = 8s. (7.98, actually).

At that time, the body travelled a distace d1 = g*t1²/2

d1 = 313.6 m.

So, now it has 9,999,686.4 m left to fall. This new distance d2 = v*t2

So t2 = 127,873.22 s.

Total time, 127,881.22 s. So, a lot. :smalltongue:





Assuming the person lands in Yale University (41.3163244, -72.9223431) or very close to there, where did they leave the shuttle? (Anything nearly impossible to calculate, I'm guessing jet streams and the like, can be ignored.)



Considering his horizontal speed as being constant at 0.89 m/s, we use the same equation that was used after he reached terminal velocity.

d = v*t

d = 113,807.16 m = 113.8 km.

So, anywhere on a radius of 113.8 km. If you know the direction that the plane was travelling (or the angle if using polar coordinates), you can find that out.


For the third part, there'd be need for the material properties as well.

[noparlpf]

Is human terminal velocity enough to heat things up enough to start burning up? I vaguely remember a what-if xkcd about hamburgers, and I think he said it was alternately seared and frozen on either side, so I'm guessing your human doesn't survive all the way down. Was that a concern? (Edit: If so, starting them closer to something resembling atmosphere might be necessary, and adding protection would help a lot.)
As for smashing a one-inch piece of concrete, yeah, probably. Concrete isn't the sturdiest of things and if I can smash that piece of concrete dropping a large rock on it from chest height I imagine the human's squishiness won't make a huge difference with the energy it's transferring into the concrete. I'm not sure if the force is the issue. I think it's the energy, and that's a fair bit of kinetic energy you're transferring into that poor piece of concrete.

[Gray Mage]

Is human terminal velocity enough to heat things up enough to start burning up? I vaguely remember a what-if xkcd about hamburgers, and I think he said it was alternately seared and frozen on either side, so I'm guessing your human doesn't survive all the way down. Was that a concern?

This one, right? (http://what-if.xkcd.com/28/). According to it, the body'd need to reach Mach 2, so with the terminal velocity that Business Scrub was considering, no.

[noparlpf]

This one, right? (http://what-if.xkcd.com/28/). According to it, the body'd need to reach Mach 2, so with the terminal velocity that Business Scrub was considering, no.

Does the human body have enough time to reach terminal velocity from 10,000 km? That's really bloody high. That steak was dropped from what, 100km? The human is accelerating towards Earth for quite a bit before hitting atmosphere. Or did I misread the height the OP mentioned?

[Gray Mage]

Does the human body have enough time to reach terminal velocity from 10,000 km? That's really bloody high. That steak was dropped from what, 100km? The human is accelerating towards Earth for quite a bit before hitting atmosphere. Or did I misread the height the OP mentioned?

Almost certainly yes, 10,000 km is really high. Way higher then the ionosfere. To put things into perspective, the guy that broke the sound barrier by skydiving jumped from a height of "only" 39 km.

[noparlpf]

Almost certainly yes, 10,000 km is really high. Way higher then the ionosfere. To put things into perspective, the guy that broke the sound barrier by skydiving jumped from a height of "only" 39 km.

I mean, to slow down to terminal velocity. If they're accelerating through 9900km of space before hitting even diffuse atmosphere, they should have broken terminal velocity and several times the speed of sound if a guy broke the speed of sound from only 39km in atmosphere. They'd probably never drop to terminal velocity, but they'd start burning up like any largeish fastish meteorite, and hit the ground with a small bang.

[Gray Mage]

I mean, to slow down to terminal velocity. If they're accelerating through 9900km of space before hitting even diffuse atmosphere, they should have broken terminal velocity and several times the speed of sound if a guy broke the speed of sound from only 39km in atmosphere. They'd probably never drop to terminal velocity, but they'd start burning up like any largeish fastish meteorite, and hit the ground with a small bang.

Oh, I'd still say very likely yes. Terminal velocity is defined as the velocity the object has when the total force on it is 0. The actuall speed'll be much higher then if it was dropped at a lower height, though.

[noparlpf]

Oh, I'd still say very likely yes. Terminal velocity is defined as the velocity the object has when the total force on it is 0. The actuall speed'll be much higher then if it was dropped at a lower height, though.

Edit: Alright, so it's still a much higher terminal velocity than if dropped from a lower height. Point being, they're going much faster than 175mph. (Which seems high anyway, as Wikipedia says that a spread-out human only falls at about 195km/hr, which is what, 122mph?)

[Gray Mage]

Doesn't terminal velocity usually mean the maximum speed at which an object can travel through atmosphere, assuming infinite atmosphere to slow down in? You hear about meteorites "slowing down to terminal velocity" or "approaching terminal velocity" or "still going way faster than terminal velocity at impact".

Terminal velocity is the speed that a certain object has when the drag, buoyancy and gravitational forces have a net force of 0. That's the formal definition.

If the object was speeding up, it'll be a maximum speed, but if it's slowing down, it isn't (if it's smaller then the initial speed, it'll be a minimum, though).

[noparlpf]

Terminal velocity is the speed that a certain object has when the drag, buoyancy and gravitational forces have a net force of 0. That's the formal definition.

If the object was speeding up, it'll be a maximum speed, but if it's slowing down, it isn't (if it's smaller then the initial speed, it'll be a minimum, though).

Darn, you got back before I edited it. Yeah, I was getting confused because there were two different things being called terminal velocity in my head and although both are they're in different scenarios.

[factotum]

I think it's a good point, though--terminal velocity depends on the drag the atmosphere is exerting on the body, so to say a body has a terminal velocity of 78.2m/s makes no sense. What altitude is it at to achieve that? 10,000km is *way* above the atmosphere, at least here on Earth, so the falling man would accelerate toward the planet at a fairly constant rate (increasing as he approached due to gravity increasing) until he hit significant atmosphere at maybe 1000km up. Not sure how to calculate his actual speed due to the non-constant acceleration, but if we assume gravity is what it is at 10,000km (about 0.15g, I think) for the 9000km trip, we'd get a speed of 5200m/s when he hits the atmosphere--easily enough for re-entry heating to fry him, and his speed in reality would be quite a bit higher due to the acceleration increasing as he gets closer.

However, this is all assuming the shuttle he's been kicked out of is hovering stationary at 10,000km, which is an extremely unlikely scenario. In reality the shuttle would be orbiting, and when he's thrown out of it, he'll go into a very slightly different orbit and never get near the planet.

[thubby]

too much missing information. where is this from and for what purpose do you need it? if you want it for a sci fi story or to get an idea of what's happening here we can probably fudge something within the right order of magnitude.

if this is a school thing your teacher has to be having you assume certain things we're not privy to. we need to know exactly what he wants you to assume.

my inclination would be to use the gravitation formula to determine its velocity at the exact point it enters the atmosphere, then treat the atmosphere (i would use 120km up) as a uniform unmoving mass of air, and switch to gravity being constant. you can determine drag from terminal velocity and get a force the atmosphere is exerting.

some basic algebra and you should have an impact velocity. as mentioned before you need the mechanical properties of the things being struck.
concrete has little resistance to sharp impact, humans can deliberately break it with hand tools. i would expect an inch of it to cave trivially.

as for the bounce. the question here is whether or not the body decelerates to terminal velocity by the time it hits ground level. if it does, then no it won't. if it's still moving at some ungodly speed then it might be enough.

edit:
this problem has a trivial answer. either this human has proper human characteristics and is destroyed on contact with the atmosphere, or it's functionally indestructible which means it destroys the concrete and either bounces or obliterates the stone.