I Newton's Second and Third Laws question

1. Aug 13, 2017

Eleni_

Hey. I have watched a video byMIT explaining the Newton laws. I have however a question. I learned that The Force that object 1 has on object two is equal to the force object 2 has on object 1. In an example with a collusion between a train and a marble we were told that the force is equal to both the train and the marble but what differs is the mass and accelaration and the Newton 2 law. If a consider a person being shot according to that, the bullet force on me is the same force i have on the bullet. The reason i will fall down to the ground is because F=ma or a= F/a. So, if i consider that i run with high speed then does that mean that i will not fall down?

2. Aug 13, 2017

phinds

Define "high speed".

If you were running fast enough then no, you would not fall down due to the immediate impact of the bullet but rather because bodily function would begin to fail. I doubt that a human can actually run fast enough, though.

3. Aug 13, 2017

Eleni_

Yes, i dont believe a human can run that Fast. It is theoritical question. But at the time of the impact i would start to decrease my speed and the bullet would start decrease her speed as well. I would drop down immediately?

4. Aug 13, 2017

A.T.

Why? Are you talking orbital speed, or what?

5. Aug 13, 2017

jbriggs444

[corrected typo in the formula]
As @phinds has pointed out, you do not fall to the ground because of the momentum of the bullet. You fall to the ground in shock, pain, nerve damage, muscle damage, bone damage or ultimately due to blood loss.

If the shooter does not fall to the ground, neither should the target -- the momentum absorbed by both is equal and opposite.

6. Aug 13, 2017

Ibix

I doubt it's quite that simple - the shooter is probably braced and prepared for the kick, while the victim probably isn't just standing in a strong stance daring the shooter to do his worst.

But basically I agree with you. According to Wikipedia (https://en.wikipedia.org/wiki/5.56×45mm_NATO) the round the M16 assault rifle fires does 945m/s and weighs 4g, for a momentum of about 3.8kgm/s. If that hits a 70kg person, conservation of momentum tells us that they'll be knocked back with a velocity of around 5cm/s. Which shouldn't bother them much. Of course, the bullet had a kinetic energy of around 1.8kJ before it hit, and the person gains kinetic energy of around 0.1J, so the vast majority of that 1.8kJ goes into smashing organs, bones, generating shock waves in soft tissue, etc. That damage is why you fall down.

If you could match speed with a bullet, of course it would do you no harm. Just as dropping a bullet into your hand, even nose first, does no harm. If you started to slow down, the question is how hard do you decelerate? If you decelerate slowly the bullet is decelerated slowly and never applies much pressure to you so never does you any harm. If you stop more or less instantaneously then it's just like you were standing still when the bullet hit you (although if you're tough enough to decelerate instantly from 945m/s and survive, I don't know why you're worried about a bullet).

7. Aug 13, 2017

FactChecker

The first fact to realize is that the movies and TV often exaggerate the impact on the target.

First of all, conservation of momentum together with the bullet slowing down means that the target will experience less momentum backward than the shooter feels kick from the gun. Then there are several additional factors to consider:
1) The momentum of the explosive gas does not (usually) impact the target.
2) The shooter is prepared to resist the kick more than the target is.
3) The kick back force may be spread over a longer time and make it easier for the shooter to resist, whereas the target is unprepared and can not resist a faster impulse.
4) Some guns redirect some gas from the gunpowder backward to reduce the kickback.
5) If the bullet goes through the target, it would not impart all its momentum to the target.
6) Conservation of momentum forces the bullet to have high velocity and almost all of the energy from the gunpowder explosion. When that energy is absorbed by the target, the "splatter" that it causes can actually make a large part of the target go forward toward the shooter. (This is the explanation of JFK's head motion when he got shot. It was replicated in tests by the Warren Commission.)

Last edited: Aug 13, 2017
8. Aug 14, 2017

Eleni_

thanks for your answers guys. All were amazing. One question however, when you are i.e to a car with x F --> and the car hits the brake, we instanty move forward following the direction of our previous v. How c
an the "splatter" makes us move backwords? Like JFK?

9. Aug 14, 2017

FactChecker

It can. It depends on the velocity and amount of matter that splatters in the direction that the bullet is going. If that velocity is high enough, conservation of momentum would force the rest to go in the opposite direction. The bullet has almost all the energy of the gunpowder explosion. If all that energy is absorbed in the target, it's almost like the gunpowder exploded inside the target. So then it depends on how the target splatters from the energy.

10. Aug 14, 2017

jbriggs444

When the car hits the brakes it begins to accelerate rearward. If the occupant pretends that the car is at rest, the perception is that he is accelerating forward. There is no instantaneous motion. Nor is there any rearward "splatter" -- at least until our heads strike the windshield.

The case of "splatter" applies when there is an impact coming from one direction and a portion of the target is scattered backward in that direction. For instance (to avoid analogies of automobile accidents and presidential assassinations) consider a sugar cube dropped into a cup of tea. The sugar cube transfers its downward momentum into cup, but there is energy left to dissipate and some of the tea is splashed upward.

The analogy to more macabre occurrences is fairly direct.

11. Nov 27, 2017

Lukeblackhill

Eleni, what happens here is a question of reference. When the bullet leaves the gun (if the distance is not too big), it will move at constant speed, undaunted by the wind resistance. When it collides with you, it will pass to you it's amount of motion (the product of its mass by its velocity), and such will create an acceleration on you. You fall because your body is not a rigid body: the part hit by the bullet will tend to move forward with the gained motion, while the rest of the body will tend to keep that same position (if you are stopped) due to is inertia. So, the part moving will "rotate" and with the help of gravity will cause your fall.

If you move with a certain speed, the referential at you will calculate the speed of the bullet not simply as v(b), but as v = v(b) - v(p), where the speed of the bullet according to you is a difference of the speed of the bullet according to the ground and your own speed. Considering that v < v(b), if you are moving, than the amount of motion the bullet passes to you when it hits will be smaller, and so the acceleration which causes you to fall. That makes your probability of falling smaller, because as your own speed v(p) gets bigger and bigger, v gets smaller and smaller, and so will be the impact of the bullet when it reaches you.

12. Nov 27, 2017

FactChecker

A lot of the effect of a bullet on a target depends on whether the bullet goes easily through the target or gets stopped inside the target.
Consider only the case where the bullet stops inside the target. Then the target absorbs all the momentum and energy of the bullet.
A bullet has a little momentum because it has so little mass. But it has almost all of the energy of the gunpowder because energy is proportional to velocity squared, which is very high for the bullet. The momentum of the bullet has a direction and will push the target back a little. The energy of the bullet is directionless, like an explosion, and causes parts of the target to go in all directions. So the primary effect on a target is as though the bullet gun powder exploded inside the target.

13. Nov 27, 2017

Lukeblackhill

Excellent reply @FactChecker. I'd like to invite you to my discussion about the problems with falling chains.

14. Nov 27, 2017

Lukeblackhill

15. Nov 27, 2017