Why is Newton's 3rd Law of Motion important in physics?

[mindfilter]

Hey guys.

I have long since realized that my interest and fascination for physics in general outweighs my mathematical skills by far. And since logic and common sense only gets you so far, I reach out to you with a sincere hope that you might help me see things more clearly.

I'll start off easy with some well known laws in classical mechanics -- Newton's laws of motion.

Newton's 3rd law of motion states that for every action there is an equal and opposite reaction. Now, if I understand this law correctly, if I was to press two identical tin cans against each other, they would, at least in theory, crumble simultaneously and similarly. Is this correct?

Does it make a difference if one tin can is in motion while the other one is not? It is my understanding that speed is irrelevant, as per Newton's 2nd law, but I might be mistaken.

Finally, are there any circumstances in which one of the tin cans would sustain substantially more damaged by the impact than the other, given that they are identical in structure and mass, and assuming the point of impact is the same for both?

Regards,
mindfilter

 

[CWatters]

Newton's 3rd law of motion states that for every action there is an equal and opposite reaction. Now, if I understand this law correctly, if I was to press two identical tin cans against each other, they would, at least in theory, crumble simultaneously and similarly. Is this correct?

Yes (although some might say it depends on the theory).

Does it make a difference if one tin can is in motion while the other one is not? It is my understanding that speed is irrelevant, as per Newton's 2nd law, but I might be mistaken.

Makes no difference.

It's very hard to find something that isn't in motion. How would you define a stationary can? Remember the Earth is spinning, moving around the sun, and the galaxy...

Finally, are there any circumstances in which one of the tin cans would sustain substantially more damaged by the impact than the other, given that they are identical in structure and mass, and assuming the point of impact is the same for both?

Yes. It's possible that the outcome is "sensitive" to very small differences. Consider two glasses bashed together. The moment one starts to shatter it stops or considerably reduces the force it applies on the other. So a very small defect/difference between the two might make a large difference to the outcome.

Consider a length of fishing line in tension. The line and the tension should be identical everywhere along it's length but it almost never snaps in multiple places at once, only in the one place that has a microscopic defect (such as a knot or abrasion might introduce).

Some quite deep theories say no two objects can ever be 100% identical right down at the atomic scale.

 

[Rap]

Some quite deep theories say no two objects can ever be 100% identical right down at the atomic scale.

But if they were, then yes, you would see them deform identically.

 

[xAxis]

I think as you are just beginning study Newton's laws, it is not good idea to examine cases with deformable objects as it can easily confuse you. Also in your example the forces are not direct, (you push cans, they push each other). It is better to think of pushing rigid bodies, frictionless suracess etc.

 

[mindfilter]

Ok, I'd like to stick with deformable objects, because my questions are related to an actual event, and it is this possible confusion I want to address.

With regard to Newton's 2nd law of motion, am I right to assume that any falling object (with no other external forces applied) with an observed acceleration equal to the gravitational acceleration (g) can not have met any resistance on its path?

Thanks,
mindfilter

 

[Rap]

Ok, I'd like to stick with deformable objects, because my questions are related to an actual event, and it is this possible confusion I want to address.

With regard to Newton's 2nd law of motion, am I right to assume that any falling object (with no other external forces applied) with an observed acceleration equal to the gravitational acceleration (g) can not have met any resistance on its path?

Thanks,
mindfilter

No - any constant mass object which does not have an acceleration equal to g is "meeting resistance" at that time. Any constant mass object which is accelerating at g, is not meeting resistance at that time. It's present acceleration tells you nothing about its past history.

 

[CWatters]

To avoid double negatives...

Lets say you drop something (initial velocity zero) off a building of height (h) and it hits the ground after time (t). You can work out the average acceleration the object experienced.

If the answer is equal to g (9.81m/s^2) then yes you can say it probably experiened no (or negligible) resistance on the way down.

If the answer is less than g some resistance was experienced.

If more than g the object was somehow propelled downwards.

Please reassure us this has nothing to do with 911 and falling buildings! It's been done to death elsewhere.

PS: Note RAPs comments about instantaneous acceleration not telling you about past acceleration.

 

[Rap]

Good point - if the average downward acceleration over a path is equal to g, then it has experienced no resistance over that path. If its less, it has.