# How are Newton's 2nd and 3rd Law Both True?

1. Feb 28, 2016

### in the rye

Hey everyone, I was reading my text and am kind of confused over Newton's 2nd and 3rd law. I understand them individually, but I don't understand how they are both true. My book covered a small portion on inertial frame of reference, which I didn't quite understand -- and I believe this may be key to understanding how they're both true.

First, to be sure, is the inertial frame of reference on Earth always Earth? They gave an example of how someone standing on roller skates on a airplane would roll backwards once it started to accelerate, therefore stating that the plane is not a good inertial frame of reference. Which, to me, seems pretty intuitive. You'd have to take Earth as your frame of reference since your body will roll backwards to remain at rest from your initial position relative to Earth.

As far as the 2nd and 3rd law, I'm confused how every action has an equal and opposite reaction if there can be a net differences in forces. In my book they said that Newton's 3rd law is what causes a rocket to lift because the ground pushes back just as much as the rocket trying to launch. But to my mind, if this is true, the rocket should just stay put because the forces should cancel out and put it into equilibrium. Obviously this isn't case from observation, but I don't really understand why, which makes me feel the rocket is more inclined to be following the 2nd law in that instance, that it's net force would be upwards, hence the lift.

However, the 3rd law also makes intuitive because if there was no equal and opposite reaction things would just fall through each other.

Can someone clear this up, please?

2. Feb 28, 2016

### cnh1995

Rocket exerts force "on" earth and earth exerts an equal force "on" the rocket. Force is acting on both of them, but only the rocket moves because of its considerably smaller mass compared to that of the earth.

3. Feb 28, 2016

### RubinLicht

I do not know frame of references well enough, so I'll leave that for someone else.
1) rocket: first of all, the fuel pushes the rocket, not the ground. Newton's third law can also be called the law of "interactions" because it basically states that a force cannot exist alone and must exist in pairs of action and reaction. I was once confused about this too. However, the action reaction forces do not both act on the rocket. If we were to take the "action" force as the resulting thrust on the rocket, then the "reaction" force is the resulting push on the fuel. So, action acts on rocket, reaction acts on fuel. There is no equilibrium.

4. Feb 28, 2016

### RubinLicht

I would like to add a clarification that in this case it's just a rocket falling towards earth or in circular motion, since we are talking about the earth rocket system and ignoring fuel.

5. Feb 28, 2016

### cnh1995

I was talking about the take-off of the rocket where it exerts pressure(by means of exhaust gases) on the ground and earth lifts it up as an equal and opposite reaction.
Sit on a matress near a wall and push the wall with your legs. The wall won't move but the matress will move in the opposite direction(with you).

6. Feb 28, 2016

### in the rye

So, in this instance, it may be more helpful to think of F=ma as Fr/mr=ar vs. Fe/me=ae where r/e = rocket/earth meaning if our forces are equal because the mass is so large the acceleration of the Earth due to the rocket is essentially so small that it appears as though the Earth isn't moving, but opposite in the case of the rocket?

I guess F=ma was what was confusing me without taking into consideration their masses, relating it to acceleration seems to clear it up a little.

7. Feb 28, 2016

### phinds

Since being under acceleration is contrary to the DEFINITION of an inertial frame of reference, that's not too surprising

[post edited to reflect my misreading of the quote]

You ask "is the inertial frame of reference on Earth always Earth?" No, there are an infinite number of inertial frames of reference. If I am moving at a constant speed there is an inertial frame of reference in which I am at rest and the surface of the earth is moving. If I change the speed, then during the time the speed is changing the frame of reference of the vehicle is not inertial but once it settles in to a new speed, it is once again inertial.

8. Feb 28, 2016

### Staff: Mentor

The rocket would rise even if the Earth's surface were not directly below it. Rocket action depends upon conservation of momentum, throwing out the exhaust gases at high speed. The momentum imparted to the exhaust must balance momentum gained by the remainder of the rocket in the opposite direction. Newton's 3rd law certainly applies here, but it's between the rocket body and the exhaust material.

9. Feb 28, 2016

### Ray Vickson

You say "In my book they said that Newton's 3rd law is what causes a rocket to lift because the ground pushes back just as much as the rocket trying to launch." I really hope your book did not say that, because it could not be more wrong. The second after the rocket leaves the ground, the ground does not "push" on the rocket anymore. The only time the ground pushes on the rocket is when it is sitting on the launch pad; the ground pushing up on the rocket is the reason the rocket does not sink through to the center of the earth.

The reason the rocket starts to move is that the gases expelled through the rocket nozzle push back against the rocket's ignition chamber, just as Newton III says.

10. Feb 28, 2016

### in the rye

Oh, my god. My mind is being blown right now. Ha. I actually feel even more confused. So, I'm guessing because of the volume of gases emitted, the gas probably has a larger mass than the rocket, which is why it accelerates? Otherwise, I don't really see how this is possible. Clearly it is, but I don't see how. Wouldn't it need a larger mass to push off of in order to accelerate? (I think its confusing because I'd imagine the gases mass would be less than the rocket's).

Even simpler examples seem confusing. If I am pushing a box with a larger mass than myself, it seems that the box should push me backwards, rather than me pushing the box forward. Maybe in this case it would be because my acceleration is larger?

11. Feb 28, 2016

### Staff: Mentor

The "equal and opposite" forces in Newton's 3rd law act on different bodies. To find the net force on an object you add all the forces acting on that object.

12. Feb 28, 2016

### phinds

What effect do you think the speed of the ejected gasses has on the overall process?

13. Feb 28, 2016

### in the rye

Combined with the comment above yours, just examining the rocket itself, it should be able to propel itself forward a certain distance. But on examining the gases, they should be propelling in the opposite direction of the rocket, which -- is what would make them 3rd law pairs? Maybe I was confused on examining the forces collectively rather than relative to a specific object... then in this instance, technically the gases could be projected further than the rocket, making the volume/masses, irrelevant unless we wanted to find the forces on the gases. However, the rocket will also be accelerated for some odd distance.