Question about Newton's Second and Third Laws

• Eleni_
In summary, the conversation discusses the impact of a bullet on a person and whether they would fall down immediately if they were running at a high speed. The experts in the conversation explain that the person would not fall down due to the immediate impact of the bullet, but rather due to the bodily damage caused by the bullet. They also discuss factors that affect the impact on the target, such as conservation of momentum, the shooter's preparedness, and the redirection of gas from the gun.
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?

Eleni_ said:
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?
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.

phinds said:
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.
Yes, i don't 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?

Eleni_ said:
So, if i consider that i run with high speed then does that mean that i will not fall down?
Why? Are you talking orbital speed, or what?

Eleni_ said:
The reason i will fall down to the ground is because F=ma or a= F/m
[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.

cnh1995
jbriggs444 said:
If the shooter does not fall to the ground, neither should the target -- the momentum absorbed by both is equal and opposite.
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.

Eleni_ said:
Yes, i don't 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?
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).

Eleni_
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.)

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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
FactChecker said:
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.)
an the "splatter" makes us move backwords? Like JFK?

Eleni_ said:
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?
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.

Eleni_ said:
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 can the "splatter" makes us move backwords? Like JFK?
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.

Ibix and FactChecker
Eleni_ said:
Yes, i don't 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?

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.

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.

Lukeblackhill
FactChecker said:
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.

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

Lukeblackhill said:
Excellent reply @FactChecker. I'd like to invite you to my discussion about the problems with falling chains.
https://www.physicsforums.com/conversations/falling-chains.137676/

Lukeblackhill said:
https://www.physicsforums.com/conversations/falling-chains.137676/
I tried to follow the link but it said that the conversation can not be found.
PS. An invite to another thread should probably be done as a message so this thread can stay on topic.

Hello!

Since my question is somewhat similar to the one originally discussed here I decided to use the existing thread.

First, the things that I consider to be true (at least generally speaking):

1) When someone fires a gun, the momentum that affects them has the same absolute value than that affecting the bullet.
2) This is roughly the reason the movies are wrong when it comes to people being shot at flying backwards
3) If the person shooting the gun is actually holding the gun, we can consider the shooter and the gun one and the same
4) Momentum equals mass * velocity

Taking all this into account, it seems to me that if the gun & the shooter were moving (let's say 'insanely fast') in a direction opposite to that of the bullet at the time of shooting, we could make the object being shot at move backwards considerably like in the movies (of course the object would have to be hard enough so that the bullet would not pass through, the bullet has a very small mass so it's velocity should be huge, the mass of the object matters etc.).

However, having looked around quite a bit, I am yet to find anything that would confirm my hypothesis. So it is quite possible that I am wrong. If so, why? And in that case, what would it take for the object being shot at to move 'backwards' considerably? The way I see it at the moment is that if the gun had immense recoil that should do it... Obviously, my belief is that the example scenario (gun-shooter moving backwards) would increase the recoil. Is this where I'm wrong and I shouldn't make the assumption?

Kaur said:
Taking all this into account, it seems to me that if the gun & the shooter were moving (let's say 'insanely fast') in a direction opposite to that of the bullet at the time of shooting, we could make the object being shot at move backwards considerably like in the movies (of course the object would have to be hard enough so that the bullet would not pass through, the bullet has a very small mass so it's velocity should be huge etc.).
If the shooter and gun are moving backwards at bullet speed before firing then the slug will come out of the tip of the gun and simply fall to the floor. The target can simply reach down and pick it up.

Yup, that's what I saw here and there... but I cannot quite get it. It does make sense but all the same I cannot quite see where my own reasoning is off.

jbriggs444 said:
If the shooter and gun are moving backwards at bullet speed before firing then the slug will come out of the tip of the gun and simply fall to the floor. The target can simply reach down and pick it up.
See for example here at 0:25:

phinds and jbriggs444
Kaur said:
Obviously, my belief is that the example scenario (gun-shooter moving backwards) would increase the recoil.
No idea how you came to this conclusion. Recoil is the change in momentum from the shot, and independent from the momentum that gun-shooter had before the shot.

If you have the shooter fire a cannonball so that it is the recoil that hurls the shooter backward then the cannonball impact on the target will indeed correspondingly hurl the target backward. Merely having the shooter fly backward for an unrelated reason has no effect on the target.

Ibix
Thank you both! At least I was on the right track as for the possible weakness in my reasoning. In short, it seems I have a cause-effect problem. Just like you said (unrelated reason). I guess I just thought too much about the m*v and what it means, forgetting what it doesn't mean.

Kaur said:
First, the things that I consider to be true (at least generally speaking):

1) When someone fires a gun, the momentum that affects them has the same absolute value than that affecting the bullet.
Yes, and as othes have said, for most guns this isn't really enough to knock you down, it would really just knock you off balance so you fall down.

One caveat here is that ultimately all of the momentum given to the bullet comes from opposite momentum transferred to the Earth, through the shooter. The shooter can deal with this in two ways:
1. Rigidly. This is better for aim and stability, but it hurts. Bracing a shotgun against your shoulder does this.
2. Softly. This is easier to absorb, but affects aim. Shooting a shotgun from the hip does this.
Taking all this into account, it seems to me that if the gun & the shooter were moving (let's say 'insanely fast') in a direction opposite to that of the bullet at the time of shooting, we could make the object being shot at move backwards considerably like in the movies...
Did you say that backwards? In order to make the victim fall backwards, you have to increase the speed of the bullet towards him, so the shooter needs to be moving forwards - in the same direction as the bullet is traveling.

A.T. said:
See for example here at 0:25:

Very cool. Thanks for posting.

There will always be more momentum given to the shooter than to the target. The shooter gets momentum from the initial velocity of the bullet and gas leaving the gun. The target only gets momentum from the bullet after it has been slowed down by air resistance in flight.

The real difference between the shooter and the target is in the amount of energy absorbed. Since the bullet mass is so small compared with the shooter mass, it takes almost all of the energy of the exploding gunpowder with it. When the bullet hits the target, the amount of energy the target absorbs depends on how much the bullet slows down inside the target. If it goes through with little reduction in velocity, then the target does not absorb much energy. If it stops inside the target, then the target absorbs almost all the energy of the exploding gunpowder as though the gunpowder exploded inside the target.

russ_watters said:
Did you say that backwards? In order to make the victim fall backwards, you have to increase the speed of the bullet towards him, so the shooter needs to be moving forwards - in the same direction as the bullet is traveling.

I wish I had :) What you say makes sense. I just got stuck with the momentum idea while obviously not quite realising what it was, hence the confusion.

jbriggs444 said:
Merely having the shooter fly backward for an unrelated reason has no effect on the target.
Although it would be a way to solve the inconsistency in movies, if the shooter would also throw himself backwards.

What is Newton's Second Law?

Newton's Second Law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In simpler terms, the greater the force applied to an object, the greater its acceleration will be, and the more massive an object is, the less it will accelerate.

What is the formula for Newton's Second Law?

The formula for Newton's Second Law is F=ma, where F represents the net force acting on an object, m represents the mass of the object, and a represents the acceleration of the object.

How is Newton's Third Law related to Newton's Second Law?

Newton's Third Law, also known as the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction. This means that the force applied by one object on another will result in an equal and opposite force applied by the second object on the first. This is directly related to Newton's Second Law because the force applied by the second object is what causes the acceleration of the first object.

What is an example of Newton's Second Law in action?

An example of Newton's Second Law is a person pushing a shopping cart. The force they apply to the cart causes it to accelerate in the direction they are pushing. The mass of the cart also plays a role in the acceleration, as a heavier cart will require more force to accelerate compared to a lighter one.

Is Newton's Second Law always applicable?

No, Newton's Second Law is only applicable in situations where the net force on an object is constant. In situations where the net force is changing, such as in a rocket launch, more complex equations and principles, such as Newton's Third Law, must be considered.

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