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"Behavior" word in the title is not very correct.

I'm in a train at a railway station and on the platform there is a glass case (the mass of case is 5 kg and if it gets hit with a velocity of 10 N then the glass will break), a frame of reference is attached to me. Now my train starts with an acceleration of $2\, m/s^2$. Now according to me I'm at rest and glass case is moving backward and so the acceleration on the glass case is $2\, m/s^2$ (at present I'm not considering the direction). Therefore the force acting on the glass case is $F=ma=5\times 2=10\, N$ at this the glass case should break, but this is not happening. Whereas according to a frame of reference attached to a person on the platform every thing is fine(i.e. there is no force(horizontal) acting on the glass case).

The law cannot be wrong and so that means that I'm somewhere wrong. I cannot find my mistake so please help me.

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  • $\begingroup$ Velocity is not measured in Newtons. And if your train is accelerating then it is not an inertial frame and F=ma does not hold in a non inertial frame. You can try to fix that with inertial forces but nothing breaks because of inertial forces. Inertial forces are fictional, they are just talked about to allow you to try to do Physics in a non inertial frame. $\endgroup$
    – Timaeus
    Commented Aug 29, 2015 at 0:19

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It's not a force that would break the glass, it's an uneven force (i.e., a baseball smacking the center of the glass).

A great illustration of this is air pressure. Air pressure has a force of about 100,000 $\frac{N}{m^2}$ - so a normal glass case big enough to hold a fire extinguisher or something would have about 10,000$N$ of force evenly distributed throughout its surface area.

If you took out all the air inside, then you would have thoursands of Newtons of force only pushing inward - most glass would shatter, strong glass may be able to withstand the force.

So when you are watching the "entire world" accelerate 2$m/s^2$ backwards, its as if the force accelerating the earth is completely evenly distributed on every particle - thus no reason for anything to break.

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  • $\begingroup$ Sir I think I have not written my problem very correctly. Assume that in place of that glass case there is a long lego structure which will fall down with even a little force(please neglect air resistance and any disturbance around the lego structure). There are two frame of reference one attached to me in the train and another one which is attached to the platform. According to frame of reference attached to me, I'm at rest and lego structure is moving with some acceleration. The product of mass of the lego and the acceleration is more than the required force to destroy the structure. $\endgroup$
    – Singh
    Commented Aug 28, 2015 at 20:29
  • $\begingroup$ (cont.) Now from my point of view the structure must have fall down but I can see that the structure is still standing. According to frame of reference attached to the platform, the lego structure is at rest and so from first law of motion the net external force is zero on the structure. Now my question is that from one frame of reference the outcome is different as compared to the other one. Why? $\endgroup$
    – Singh
    Commented Aug 28, 2015 at 20:35
  • $\begingroup$ My question answers that exactly. There is no such thing as "even a little force destroys" anything. It is force differential NOT force that can destroy anything. $\endgroup$
    – Señor O
    Commented Aug 28, 2015 at 20:36
  • $\begingroup$ Additionally, a force doesn't necessarily cause a structure to fall down, a torque does. If force is distributed evenly, there is no torque $\endgroup$
    – Señor O
    Commented Aug 28, 2015 at 20:37
  • $\begingroup$ $ma$ is not a force. It is the product of mass and acceleration. That value will be vectorally equal to the sum of real forces, but it is not the force. As @SeñorO states, forces by themselves don't break things. You must consider how a real force is applied, including the time interval (for momentum change), the displacement (for work), application location (for torque), and the area (for stress calculations). $\endgroup$
    – Bill N
    Commented Aug 28, 2015 at 21:39
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You are calculating an unreal force by using Newton's second law. Remember that Newton's laws are valid in inertial frames of reference. And Newton defined inertial frames as those frames where an object continues to be at rest or in constant motion unless acted upon by a real physical force.

In your example the train or you is not an inertial frame. Hence, calculating $F$ from $F=ma$ for the glass case is invalid for the glass case is not acted upon by any real force. You cannot say a force of that much newtons is acting on it. When a real force acts on a body and causes an acceleration then only you can calculate the force by knowing the mass and the acceleration and this happens in inertial frames.

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  • $\begingroup$ Till now I wasn't knowing about inertial frame of reference. Now I'm trying to understand it. Thank you for your answer. $\endgroup$
    – Singh
    Commented Aug 30, 2015 at 2:17

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