Interesting gravity question

[Peppersrule]

Hi

I'm a first year Physics Undergrad and I never quite got satisfied with the answer to this question:

"Why would you be rather hit with a pillow than a rock, if they reach the ground at the same time?"

I know the obvious answer is because the pillow is soft. But how would you describe this using proper physics? One answer that is provided is: "The pillow is softer, so it travels through a greater distance as it comes to rest. The pillow therefore has a smaller magnitude of acceleration than the rock, and the stopping force on the pillow is less."

I do not understand this version of explanation. Could someone please clarify this for me?

Thanks

 

[WannabeNewton]

Hint: Impulse. How would the impact time for a run of the mill pillow compare to the impact time for a rock?

 

[Peppersrule]

It would be greater for the rock than a pillow? Also! By Newton's 3rd law since my head would exert less force on the pillow, the pillow would also exert less force on my head, because of the smaller impulse. Is that valid?

 

[Peppersrule]

The line I'm having trouble with is, "The pillow ... travels through a greater distance as it comes to rest"

 

[WannabeNewton]

Wouldn't you agree that the pillow has a noticeably longer impact time than the rock? Doesn't the pillow take much longer to compress to rest upon impact than the rock does? How will this then affect the average force exerted by the pillow during impact compared to the average force exerted by the rock during impact?

 

[Peppersrule]

That kind of makes intuitive sense now that you mention it. I guess I had a slightly wrong idea of impulse. I'm starting to grasp it now...
Longer compression time = "greater distance as it comes to rest", and hence the smaller magnitude of acceleration as it takes more time

I think I'm on track now. maybe

 

[TurtleMeister]

Imagine you are driving a car and you come to a stop sign. In scenario one you begin applying breaks 200 feet away from the sign. In scenario two you begin applying the breaks 50 feet away from the sign. You feel the force on your body as you're coming to a stop. Which scenario produces the greater force?

 

[Peppersrule]

The latter

 

[TurtleMeister]

The latter

Okay, so in which scenario does the car have the greater acceleration (de-acceleration same thing)? And what does Newton's second law have to say about that?

 

[Peppersrule]

The latter will have a higher acceleration and thus by Newton's 2nd law, a greater force.

Thanks!

 

[georgir]

It has little to do with "its soft", more with "amount of motion", or momentum, and the fact that it will be preserved, i.e. if it is removed from the falling object, it is being transferred to your head.

Wannabe is also right to turn your attention towards impulse, which is the rate of change of momentum on one hand, and is force multiplied by time on another.
One last hint: you have approximately equal interaction duration, or even, if you still want to make your "soft" point, higher duration with a more elastic interaction; mass of your head equal in both cases.

EDIT: I'd still ignore the "soft" side of things, and focus mainly on the differences in mass, and thus momentum, as that effect is much more pronounced in this case.

EDIT 2: You can even have a rock that crumbles such that the interaction time really is no shorter than the pillow case. Or a rock with a pillow attached to it. It would still not save you. So most definitely ignore the "soft" part.

EDIT 3: On the other hand, you can also have a very small rock, with mass comparable to the pillow mass... I guess you might have to bring up both aspects after all.

EDIT 4: Especially considering the provided answer, which I totally didn't pay attention to while writing all of the above...

 

[Lsos]

Besides the longer impact, I think the greatest benefit of a pillow, which wasn't yet mentioned, is its surface area. It is much greater than the rock, and so the pressure exerted on you from it will be MUCH less. Not only that, but its softness and flexibility gives it an even greater effective surface area. I suspect the actual deceleration time is a much smaller effect than this.

 

[SteamKing]

First Law of Fluffiness: You can fluff a pillow; you can't fluff a rock.

 

[Oldfart]

Hi

I
"Why would you be rather hit with a pillow than a rock, if they reach the ground at the same time?"

I don't see how there is an answer to this without more information being supplied. For instance, was the pillow given a high velocity throw to the ground so it could catch up with the falling rock? In some circumstances, the pillow blow can obviously be more severe.