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So I was thinking about Newton's third law for sometime lately, and my problem is more about the concept, I'm fine with solving problems. I thought of these scenarios and tried to apply Newton's three laws on each and now I'm even more confused. My goal here is to assure if the force experienced by both of the fly and the train is the same in these scenarios: For all of these assume a train and a fly facing each other on a certain axis also neglect any external field forces and assume both of the fly and the train as particles(neglect deformation)

  • Dynamic fly collides with a static train

  • Dynamic train collides with a static fly

  • Dynamic train collides with dynamic fly

My answer to these is yes,no,no respectively. What do you think?

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closed as off-topic by Aaron Stevens, ZeroTheHero, Kyle Kanos, Jon Custer, glS Jan 31 at 12:39

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    $\begingroup$ Why would the first and second not be the same? Aren't the situations identical and just reversed? That being said, when you say "My goal here is to assure if the force experienced by both of the fly and the train is the same in these scenarios" then remember that no force exists alone. All forces come in an action/reaction pair. They are never alone. So that makes it quite easy: if nothing else applies force, then the force on the fly and train must be the same always. Regardless of how any of them are moving at that moment. $\endgroup$ – Steeven Jan 28 at 15:46
  • $\begingroup$ To my understanding the train is capable of applying a force equal to the fly's while the fly isn't capable of doing the same, I mean for the second and third ones my guess is that there will be a resulting net force in the direction of the train which is F(net) =F(Train) - F(fly),(sorry for not using mathjax) $\endgroup$ – user597368 Jan 28 at 15:54
  • $\begingroup$ I think yes, yes, yes. One way to think of it is that the physical laws are the same in all intertal frames. This is not maybe not the first thing one learn in physics, and may sound abstract, but it is a very powerful tool! $\endgroup$ – B. Brekke Jan 28 at 15:56
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    $\begingroup$ the law is universal, so the answer is yes in the three scenarions $\endgroup$ – Wolphram jonny Jan 28 at 17:31
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    $\begingroup$ @user597368, one more comment. When I was teaching high school physics, I went over several examples just like the fly-train problem, and students seemed to understand the concept on that particular day. However, INVARIABLY, there were some students who reverted back to their misconceptions on test day, and missed the Newton's 3rd law questions on the test. Some people just want to hold onto their misconceptions, even when they have direct evidence to the contrary in front of them. You can't properly learn physics is you insist on doing this. $\endgroup$ – David White Jan 28 at 17:36
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Yes, yes, and yes.

The problem is that your comment “To my understanding the train is capable of applying a force equal to the fly's while the fly isn't capable of doing the same” to Steeven is incorrect. The forces are equal and opposite, but obviously the effect of the forces are not. Before considering the three scenarios, consider the following.

Let the force on the fly be $F_{fly}$. The acceleration of the fly is then related to $F_{fly}$ by Newton’s second law,

$$F_{fly}=m_{fly}a_{fly}$$

And the acceleration of the train is related to the force on the train, $F_{train}$ by Newton's second law,

$$F_{train}=M_{train}a_{train}$$

From Newton’s third law,

$$F_{train}=-F_{fly}$$

Therefore

$$m_{fly}a_{fly}=- M_{train}a_{train}$$

And

$$a_{train}=-\frac{m_{fly}a_{fly}}{M_{train}}$$

$$a_{fly}=-\frac{M_{train}a_{train}}{m_{fly}}$$

Since $M_{train}>>>m_{fly}$, $a_{train}<<<a_{fly}$ and the affect of the fly on the train is miniscule compared to the effect of the train on the fly.

Now let’s consider the three scenarios

-Dynamic fly collides with a static train

Based on the equation for the acceleration of the fly, the dynamic fly undergoes a large deceleration compared to the train's acceleration upon impacting the static train. Based on the equation for the acceleration of the train, the static train undergoes a miniscule acceleration compared to that of the fly due to the impact of the dynamic fly.

-Dynamic train collides with a static fly

Based on the equation for the acceleration of the train, the dynamic train undergoes a miniscule deceleration compared to that of the fly upon impacting the static fly. Based on the equation for the acceleration of the fly, the static fly undergoes a large acceleration compared to the acceleration of the train due to the impact by the dynamic train.

-Dynamic train collides with dynamic fly

The equations still apply but what happens will depend the relative velocities of the fly and the train. For example, if they are both going in the same direction, and the velocities are nearly the same, the force each imposes on the other will be small (and the fly might even survive!).

After the fly and train collide and stick together, the two objects can be considered as one and will have the same acceleration $a$ where $a$ is

$$a=\frac{F}{m+M}$$

And $F$ is the external force applied to combination of the train and the fly.

Bottom line, Newton’s third law does not nullify Newton’s second law. Newton’s second law applies to each object individually. Newton’s third law simply means that forces do not exist in isolation.

Hope this helps

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  • $\begingroup$ I think I'm close to getting it, thanks. So does this mean that for the first case the train is going to get accelerated and probably move towards the fly even if for an infitesimal time, also a side note that I denoted that both of the fly and train face each other (so they would move toward each other in the third case) but I think this still follows the same pattern of deceleration for the train and acceleration for the fly. $\endgroup$ – user597368 Jan 28 at 18:12
  • $\begingroup$ @user597368 Yes the train gets accelerated but given the ratio of the masses it would be for all practical purposes immeasurable. Sorry I missed the side note. $\endgroup$ – Bob D Jan 28 at 18:22

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