Falling to the ground vs. a flat surface hitting you (same speed)

Factual Questions
1

I was wondering if I am applying Newton’s third law correctly in comparing first, a situation where a person falls down to the ground at some speed, let’s say 140 mph, and second where another person who is standing up (i.e. is stationary) is hit with a truck moving at the (same) speed of 140 mph; assume the front of the truck that hits the person has a flat, square face whose hardness and other properties are, for all practical purposes, identical to those of the ground that the first person fell to.

The question is whether the force exerted by the ground on the first person and the force exerted by the truck on the second person will be the same.
If so/not so, then why?

Also, is there any weight of the truck for which the force will be equal? (in other words, if the “truck,” had the mass of the Earth, would the Earth hitting the stationary person, from the side, then be equal to the person falling downwards to the actual earth?) If not, then why is Newton’s third law not violated, because in this specific case, we have a person falling to the earth and the earth hitting the person at the same speed (meaning, why do these situations fall outside the applicability of Newton’s 3rd law)?

2

I don’t think there should be any significant differences between: Falling to the ground and going splat, or: being stationary and being hit by a planet (including its atmosphere).

The air resistance/cushioning effects might be different for a truck though, because (unlike a planet), some of the air it is trying to push at you is escaping off to the sides.

3

Of course there is a huge difference. The kinetic energy in the first case is (1/2)*mass of man * (140mph)^2 and in the second case the kinetic energy is (1/2)*mass of truck * (140mph)^2. Unlike Momentum, Kinetic energy is not conserved in inelastic collisions (or soft body collisions).

4

You can’t just look at the starting kinetic energy and tell anything from that. In the first case, if we use the frame of reference of the falling man, the kinetic energy is then (1/2)*mass of Earth * (140mph)^2 which is way larger than the kinetic energy of the case with the truck.

For the OP, there’ll probably be differences on the order of (mass of man) / (mass of truck), or possibly that quantity squared. For a heavy truck, that will be small.

5

The force from the truck will be a little less than the force from the ground; my WAG about 2-3% less. On hitting the ground, you have to add 1 G because gravity is pulling you into the ground, but not into the truck. Also, the truck will decelerate on impact by a factor of the mass of the truck divided by the combined mass of the truck + person. So for a 200 lb man hit by a 10,000 lb truck, the final velocity will be reduced by ~2%.

I that case, the force would the same. A truck with the mass of the earth would pull a person into it at 1 G.

6

Either way, it’s going to leave a mark.

7

In Russia, Black Earth hits YOU!

8

You seem to be presuming that all the truck’s energy will be dissipated in the collision - which is definitely not the case. What’s relevant is the change in velocity of the man (and how rapidly it changes).

9

There’s some room for nitpicking, but they’re practically the same.

Main nits:
At the end of the impact the Earth will still be acting on the man with a 1G force, while the force from the truck will be zero once man and truck are travelling at the same speed.
The truck will be slowed down slightly by the impact.

Both of these contribute to making the impact with the Earth the worst, but they’re not significant (Depending on the level of accuracy you’re aiming for).

Tiny nits:
The acceleration of the truck and the Earth due to the man’s gravitational pull.

10

Fair enough

Thats not relevant either.

Conserving momentum tells you very little in this case or cases involving inelastic collisions. A 10 g bullet travelling at 1000 m/s hitting you and a 10,000 g (22 lb) child bumping against you at 1 m/s may bring about the approx the same momentum change or velocity in you - but I’ll advise you take the latter over the former.

In fact, Newtonian physics is not very helpful in cases involving inelastic collisions since it only tells you that momentum is conserved and not much else. It considers bodies as rigid masses. In my opinion, this is what’s relevant here :

Case A - Man falls to ground at 140 mph

A.1 –> Whats the orientation on man hitting the ground ? (i.e how much of the area comes into contact initially. The overall forces are predicted by Newtonian physics but the Stresses are not - the stresses on the ground surface and the man’s body are function of contact area

A.2 —> How does the stress propagate through the body and the ground

A.3 —> How is the released kinetic energy accommodated - earth surface deforms, bones deform break, skin torn , muscles torn , sound , heat , …

Case B - Truck travelling at 140 mph hits stationary man

B.1 –> Whats the orientation of man hitting the truck ? I doubt you can recreate the same contact area as in case A. In all probability, the truck only hits the man on the upper part of his body and now the stresses there are higher. Also - the truck surface is different than the ground surface. The stress pattern on the body is totally different now and probably involves torsion too since the feet will see friction.

A.2 —> How does the stress propagate through the body and the truck surface. Stress will propagate differently in the body since only the upper part is hit. The truck will propagate stress differently too since it may have bumpers designed to absorb shock and so on…

A.3 —> How is the released kinetic energy accommodated - truck bumper deforms, bones deform break, skin torn , muscles torn , sound , more heat due to friction …

11

I tend to agree but I want to see Mythbusters do this.

12

From the OP

In both these cases, one very hypothetical, the man will have his velocity changed by 140 mph is a fraction of a second. There really is very little difference between the two situations when examining the moment of impact.

13

I believe you are thinking the man as a rigid body when it is not. Different parts of the man will end up with different velocities. The moment of impact is very different and the stresses at the moment of impact are different too.

14

Agreed. What I was trying to imply is that the accelerations - and thus the forces - on the person will be much the same in both the falling and the hit-by-truck cases.

How so? All parts of the man’s body change velocity by 140 mph in a small fraction of a second.

15

Are you still claiming huge differences? It sounds like you’re just picking nits now.

16

The primary difference, all other things being equal, is that a man hitting the ground at 140mph is accelerating at the time. Moments before he hit the ground, he was going slightly less than that, but the impact occurs during an acceleration event which does not exactly end with impact. This is covered in several previous posts, that the earth is exerting 1G or so on the man (ever so slightly less if he is hitting the ground in the Tibetan Plateau at 17000 feet or so). The speed of the truck can be treated as a constant, so the impact happens with a flat speed curve with no positive acceleration, and as others have said, probably a very small deceleration. Ultimately, though, the difference is vanishingly small.

17

Not necessarily. According to what I’m finding online, the terminal velocity of a skydiver prone in relations to the ground is about 125mph. So if he is in free fall and at 140 when hitting the ground, it would suggest he was in the process of decelerating back down to terminal velocity.

But if he was coming down feet or head first he may have still been accelerating.

18

There’s a good chance he wasn’t: The terminal velocity of a human body falling through Earth’s atmosphere depends on the body’s orientation, but is generally reckoned at around 120 mph. So a body that hits the ground at 140 was likely doing something close to that speed for some time before impact.

ETA: scooped by obfusciatrist

19

Sounds like ? Claiming ? That is so patronizing !!

Have you conclusively proven that they are the same ?

20

You certainly claimed there would be a “huge difference” in post 3.

Now you’re talking about differences that are really no bigger than the differences you might see between two different people hitting the ground, or the difference between two different people getting hit by a truck. So yeah, that does sound like a nit to me.

I and others have already said there’d be small differences. That falls out of the math for partially elastic collisions.