LIL 5 year old boy falling a 50 feet to another persons arms

[kadaj6]

Homework Statement

The 37lbs(16.78kg) baby falls from a 50feet(15.2m) building, The baby's Δx on the mans arms is 1m.

I already got his velocity and acceleration during the 1m he is on the mans arms.

a(during the time the baby is on his arms)=150m/s/s v(inicial)=17.3m/s

I said that the force made by the person is F=2353N

The question are,

1.At what height would the man would not be able to save the baby boy?
2.What is the minimum Δx in the mans arms that would guarantee no injuries on the baby?
3.Why was the baby boy saved and not a miracle?
4.why did the man experienced back pain after the incident?

ok those are my final questions, i already did most of it, since the only variables given by the problem are initial height baby weight, and Δx on mans arms.

sorry for my bad English, if you don't understand something let me know.

 

[kadaj6]

please if anyone can help, or doesn't understand something let me know I am waiting here, this was a real life problem here where i live, and i have to analyze it, but I am really stuck

 

[kadaj6]

anyone?

 

[Pkruse]

You don't show your work, but I got a similar answer.

 

[PhanthomJay]

I don't know about your calcs for the force, but the answers to your questions require knowledge of what impact forces can be withstood by parts of the human body.

 

[kadaj6]

Yea that's what i though, i guess i have to check that out, let me get home and show you my calc for the first couple of things to make sure everything is ok

 

[kadaj6]

1.for V i said that:
where Δx is 15.2m
a is gravity since its free fall
(2*Δx*a)^1/2=V
V=17.3m/s
this means that the initial velocity when the baby reaches the mans arms is 17.3m/s

2.Then i look for how much time was the baby decelerating on his arms:
i used S=[V(initial)+V(final)/2]*t
since the man was 1m from the floor S=1m V(final)=0 V(initial)=17.3m/s
solve for t and u get 0.12s.

3. FOr the acceleration felt by the baby on his hands i used:

a=[V(final)^2-V(initial)^2]/[2*Δx]
Δx=1m
i get that a=150m/s/s

4.So when i look for the Force made by the man i get (saying that down is + and up is -)
W-F=MA
F=-MA+W

W being weight 164.6N
m being mass/inertia 16.78kg
a=150 m/s/s
i get F=-2353

Do i have all this initial calc correct so i can start looking into the other questions i gave on the first post?

 

[PhanthomJay]

This is very good until you get to the end. In which direction is the net force on the child?

 

[kadaj6]

force of the child which is his weight goes down, but since i chose down as + is positive

 

[kadaj6]

ived searched everywhere on the internet for average force withstood by a 37lbs pound boy, and average force that an average man can make with his hands.

Don't know where else to look for, lol this professor is killing me

 

[PhanthomJay]

First your calc for the force on the child is wrong. The child's weight acts down and the force exerted on him by the man acts up. Now which way does the child accelerate, up or down? The net force is always in the direction of the acceleration. You must be very careful with the use of plus and minus signs.

 

[kadaj6]

well, the a i used was the one felt by the boy on the mans arms, I am thinking its negative since its the one that makes him stop, am i wrong?

 

[PhanthomJay]

well, the a i used was the one felt by the boy on the mans arms, I am thinking its negative since its the one that makes him stop, am i wrong?

Acceleration is not a force. It is a rate of change of velocity caused by a force. The acceleration is indeed up, or negative by your convention. It is easier to choose up as positive, because of that pesty plus and minus sign, but let's stick with your convention that up is negative. Now use Newton's 2nd law, and try your calc again. And when the minus sign blows you away again, as it often does, try up as positive , and see what you get. Your answer is wrong.

 

[kadaj6]

now it gives me a positive value of 2681.6N which i find that it's incorrect since the force made by the man to carry the boy is upward(negative)

 

[kadaj6]

here is a STELLA simulations of the problem its in spanish, I am sorry but i think ull be able to understand "Altura de bebe" means the position of baby. Check them out and let me know if you see anything wrong with them.

 

[PhanthomJay]

now it gives me a positive value of 2681.6N which i find that it's incorrect since the force made by the man to carry the boy is upward(negative)

That answer is correct. The plus and minus sign often gets the best of us. Choose up as positive, and draw a free body diagram of the baby. His weight acts down. The force of the man's hands on him acts up. We write Newton 2 as:

[itex]F_{net} = ma[/itex]
[itex]F -W = ma[/itex]
[itex] F = ma + W[/itex]

Now if you choose up as negative, it's a little harder with that minus sign, but anyhow

[itex]F_{net} = ma[/itex]
[itex]W- F = -ma[/itex]
[itex] F = ma + W[/itex]

Same result. Convince yourself. Not that easy sometimes.

 

[kadaj6]

thankyou!

 

[PhanthomJay]

If I scale and interpret that graph correctly, it appears to indicate that la fuerza agrees with your (and Pkruse) original answer, but I don't know why. Could be a book error??

I was curious about the survivable impact force on a child and searched the web with some mixed results. One source talked about 50 g's (50 times his weight, or about 8000 N), causing death or serious injury. Another talked vaguely of 10g's (1600 N) being a limit without serious injury. There are so many variables it is hard to determine.

Without getting too philosophical or religious, note that miracles and physics, in my opinion, are never in conflict. The laws of Physics as we know them are not violated. Physics can answer the question as to what happened, but not why it happened. The real miracle may have been in the man being there at the right place at exactly the right time, and having caught the baby at its stomach and not its neck. Physics cannot determine the randomness of this event. Whether or not this random event is miraculous, I leave this to the reader to decide.