# Stuck in understanding Newton's 3 laws

• I
Clockclocle
I'm stuck to understand 3 laws of Newton. It doesn't make sense to me.
1. Suppose the case when a person stay in a rest vehicle.When we accelerate the car the person still at rest so the person has to move to the tail of the vehicle cause his intertia of staying rest. If we decrese the acceleration to negative immediately, does it give the person a velocity? Cause he move to the head of the car and the car tend to stop.
2.Does the big intertial cause a big time to change the state of motion? When I push an empty box it seem immediately move but if I push a fullfill box it take a little bit of time to start moving.
3. When I push a book to hit another, why it still move a little bit when the second book applied the same force but negative direction? it should be stop or going backward.

## Answers and Replies

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Perhaps we should start with Newton's first law:

Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.

What do you not understand about that?

topsquark
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1. There is no absolute rest and the firat law does not treat absolute rest. It states that an object not acted upon by a force remains at rest or in constant rectilinear motion. When the car decelerates, the person will keep moving at the speed it was moving (ie faster than the decelerating car) - unless acted upon by a force.

2. Large inertia means lower acceleration so larger time to reach the same speed. However, what you are experiencimg is more likely the reault of larger friction and therefore a need for more force for the big box to start moving in the first place.

3. First of all, you are not applying the law correctly. The force from the other book on the first is not the third law pair of the force with which you push the book. The third law pair of the force from you on the book is the force from the book on you. Second, in a static situation the sum of all forces on an object is zero so the force from the second book on the first must be opposite in direction and equal in magnitude to the force with which you push if there is static equilibrium. This will also result in the book being squeezed togeter, expulising any air that was filling gaps between pages. This is likely what you experience as the book moving as both books will compress a little.

topsquark
Clockclocle
1. There is no absolute rest and the firat law does not treat absolute rest. It states that an object not acted upon by a force remains at rest or in constant rectilinear motion. When the car decelerates, the person will keep moving at the speed it was moving (ie faster than the decelerating car) - unless acted upon by a force.

2. Large inertia means lower acceleration so larger time to reach the same speed. However, what you are experiencimg is more likely the reault of larger friction and therefore a need for more force for the big box to start moving in the first place.

3. First of all, you are not applying the law correctly. The force from the other book on the first is not the third law pair of the force with which you push the book. The third law pair of the force from you on the book is the force from the book on you. Second, in a static situation the sum of all forces on an object is zero so the force from the second book on the first must be opposite in direction and equal in magnitude to the force with which you push if there is static equilibrium. This will also result in the book being squeezed togeter, expulising any air that was filling gaps between pages. This is likely what you experience as the book moving as both books will compress a little.
1. I mean when the person stay rest at the first and the car accelerating then he still stay at rest, but when the velocity become large vmax. What if we decrease the acceleration immediately? (change the acceleration by some ways ) does it immediately give the person velocity vmax? cause the car tend to stop but the person tend to move out the vehicle according to many experiments.

PeroK
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1. I mean when the person stay rest at the first and the car accelerating then he still stay at rest, but when the velocity become large vmax. What if we decrease the acceleration immediately? (change the acceleration by some ways ) does it immediately give the person velocity vmax? cause the car tend to stop but the person tend to move out the vehicle according to many experiments.
Have you ever been in a car?

topsquark and russ_watters
Clockclocle
Have you ever been in a car?
yes.

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yes.
It sounds like your experience is very different from mine. I don't recognise your description of car travel.

topsquark and russ_watters
Clockclocle
It sounds like your experience is very different from mine.
I read it from the book but I don't understand when we combine (a) and (b) it seem like the man gain velocity.

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I read it from the book but I don't understand when we combine (a) and (b) it seem like the man gain velocity.View attachment 315611
You should have posted that in your original post. That's not what traveling in a car is like. You have seats that push you forward with the car. That's more like being on roller skates in an empty freight car.

topsquark
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I read it from the book but I don't understand when we combine (a) and (b) it seem like the man gain velocity.View attachment 315611
You can do this experiment if you have a marble and a biscuit tin. Put the tin on a flat table and the marble in the middle of the (clean, empty) tin and make sure it doesn't roll on its own (i.e. that the bottom of the tin is flat, not curved). Without lifting the tin at all, slide it sharply (i.e. quickly and with rapid changes of direction) backwards and forwards on the table.

Ideally, the marble will stay in one place relative to the table (a piece of tape on the table to mark the initial location of the marble will help). In practice there is some friction, so it will actually start to move in the same direction as the tin, but if you move the tin reasonably sharply and take care to only slide the tin you will find that the marble moves much less than the tin. A video camera so that you can freeze frame and see how far you are moving the tin and how far the marble is moving may help.

As PeroK says, this is a very different experience from traveling in a car. In that case you have chairs and seat belts specifically designed to stop you from sliding around relative to the car, even under the high accelerations you may encounter in the event of a crash.

Last edited:
topsquark and PeroK
Clockclocle
You should have posted that in your original post. That's not what traveling in a car is like. You have seats that push you forward with the car. That's more like being on roller skates in an empty freight car.
Sorry for wrong question. Actually I don't understand the picture. When the vehicle accelerate to some large velocity (picture A) then immediately decrease the acceleration why the person change from stay at rest to continue moving ?

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Sorry for wrong question. Actually I don't understand the picture. When the vehicle accelerate to some large velocity (picture A) then immediately decrease the acceleration why the person change from stay at rest to continue moving ?
Because they hit the back wall of the freight car?

topsquark and russ_watters
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Sorry for wrong question. Actually I don't understand the picture. When the vehicle accelerate to some large velocity (picture A) then immediately decrease the acceleration why the person change from stay at rest to continue moving ?
a) and b) look like two different, unrelated scenarios. They are not different phases of the same motion.

topsquark
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So the hit give him velocity ?

Clockclocle
Because they hit the back wall of the freight car?
So the hit give him velocity ?

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I'm stuck to understand 3 laws of Newton. It doesn't make sense to me.
1. Suppose the case when a person stay in a rest vehicle.When we accelerate the car the person still at rest so the person has to move to the tail of the vehicle cause his intertia of staying rest. If we decrese the acceleration to negative immediately, does it give the person a velocity? Cause he move to the head of the car and the car tend to stop.
First of all it is very important to be clear about the fact that there's no absolute space, although that's what Newton proposed, but in this case Leibniz was right. First of all you need a spacetime model and a definition of a frame of reference. In Newtonian mechanics you postulate an absolute time, i.e., the existence of clocks that tick at the same rate, no matter, what happens to them (that's an idealization of course, but the best such clock are the atomic clocks used today to define the unit of time, second, in the SI unit system; maybe not too long from now there'll be even more robust nuclear clocks). Further it is assumed that space is always described as the usual Euclidean space you are used to from your math classes in school. So a reference frame can be simply constructed by using three rigid rods, defining a Cartesian basis system and a reference point, against which you can measure positions of material points and describe there motion as a function of time, as measured by an ideal clock, relative to the so defined reference frame.

Concerning Newtonian dynamics, everything starts with the 1st postulate, which in modern terms simply says that there exist inertial frames of reference, where a particle stays at rest or in rectilinear uniform motion, if it is not interacting with any other particles. In other words, relative to an inertial frame of reference the velocity of a particle, which doesn't interact with anything else, stays constant.

Whether or not a given reference frame is an inertial frame can only be established by observation. Usually we just use a reference frame at rest relative to the Earth and take into account that there's the gravitational interaction of the bodies under investigation due to the gravitational field of the Earth. This seems to be an inertial frame of reference to a not too bad approximation. On the other hand, it's clear that it is unlikely that the Earth, which is rotating around its axis (relative to a reference frame, defined by the fixed stars) to define precisely an inertial frame, and indeed as the famous Foucault-pendulum demonstration shows, the Earth-rest frame is indeed not exactly an inertial frame of reference. The rest frame of the fixed stars turns out to be a better one. The best inertial frame we have is the rest frame of the cosmic microwave background.

Having established an inertial reference frame (with a precision sufficient for the purposes of your application), you can turn to Newton's 2nd Law, which defines mass and force in a quasi-axiomatic way: Mass is a measure for "inertia", i.e., it describes how much "effort" it takes to change the velocity of a body. Newton defined it as being proportional to the "amount of matter", i.e., the mass of a body of a given material twice as large as another of the same material should be twice as large too. Given that measure for inertia, the acceleration of the body depends on the applied force according to ##\vec{F}=m\vec{a}##.

Finally there's Newton's 3rd Law, which deals with a very general property of interactions, i.e., forces acting between several bodies. The most simple case are socalled two-body forces, an that's also the only kind of forces Newton indeed considers. The 3rd Law then says that, if there are two bodies, and there's an interaction between these two bodies such that this interaction imposes on particle 1 a force ##\vec{F}_{12}## due to the presence of particle 2, then the interaction imposes on particle 2 a force ##\vec{F}_{21}## due to the presence of particle 1, and ##\vec{F}_{21}=-\vec{F}_{12}##.

Using these postulates, the other great achievement of Newton, was the general law of the gravitational interaction, i.e., that between two "point-like bodies" there's an interaction force
$$\vec{F}_{12}=-\vec{F}_{21}=-G m_1 m_2 \frac{\vec{x}_1-\vec{x}_2}{|\vec{x}_1-\vec{x}_2|^3},$$
where ##G## is a constant (the Gravitational constant) and ##m_1## and ##m_2## are the masses and ##\vec{r}_1## and ##\vec{r}_2## are the position vectors relative to an arbitrary inertial frame of reference.

2.Does the big intertial cause a big time to change the state of motion? When I push an empty box it seem immediately move but if I push a fullfill box it take a little bit of time to start moving.
3. When I push a book to hit another, why it still move a little bit when the second book applied the same force but negative direction? it should be stop or going backward.

topsquark
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So the hit give him velocity ?
There was a thread recently where I said I didn't like physics being taught with "unrealistic" scenarios. I think your book is the sort of thing I was talking about. If you are standing on a stationary bus and the bus accelerates, then either you get pulled forward by the bus (through friction on your feet or by holding on to something); or, if there is nothing to hold onto and the bus accelerates too quickly, your feet get pulled out from under you and you fall over backwards. What you don't do is remain at rest relative to the ground outside and slide to the back of the bus. An empty drinks bottle lying on the floor might do that, to some extent.

So, the physics presented in your book seems unrealistic to me. Newton's first law, in terrestrial scenarios, is actually quite hard to see (which is why it evaded the Greeks and the Romans and it took the genius of Isaac Newton to identify it).

The author of that book seems to be pretending that Newton's first law can be seen easily on Earth. Which is simply not true. Even in the example @Ibix gave of a marble in a tin, the marble does not remain at rest relative to the table, as there is inevitably a friction force between the marble and the tin (even if this force is quite small).

The best example of Newton's first law is something like the Voyager spacecraft , that continues through empty space at an almost constant velocity almost indefinitely, where it is not slowed down by the external forces that are inevitable here on Earth.

topsquark, Ibix and vanhees71