Why don't we consider Earth's forces/movement in problems?

[alkaspeltzar]

According to N3L, every time we move or apply forces, there is a reaction. Therefore, walking, driving and stopping would all affect Earth right?

Then why don't we have to consider that in our physics problems? Wouldn't falling down to Earth's surface mean Earth was moving towards us too, so wouldn't the force be different than if we just fell onto an immovable object?

I know Earth is big, but still it wouldn't it matter? I know this is elementary, but i has my brain questioning and wondering. So insight would be appreciated.

 

[russ_watters]

You could, if you want, include movement of Earth in such a problem, but it is usually ignored because it is so small.

...why don't you try calculating the acceleration and motion of the Earth for a 100kg mass dropped from 1m and see just how small?

Or, maybe, flip it over and calculate how much mass is required for a 0.1% threshold of relevance?

 

[PeroK]

Then why don't we have to consider that in our physics problems? Wouldn't falling down to Earth's surface mean Earth was moving towards us too, so wouldn't the force be different than if we just fell onto an immovable object?

I know Earth is big, but still it wouldn't it matter? I know this is elementary, but i has my brain questioning and wondering. So insight would be appreciated.

If it did matter, then you would have to take into account everything happening around the world: everyone driving, walking, jumping in all different directions.

 

[alkaspeltzar]

You could, if you want, include movement of Earth in such a problem, but it is usually ignored because it is so small.

...why don't you try calculating the acceleration and motion of the Earth for a 100kg mass dropped from 1m and see just how small?

Or, maybe, flip it over and calculate how much mass is required for a 0.1% threshold of relevance?

i did a calc...based on force applied to the Earth based on force applied to 100kg block via gravity. Yeah values 10^-24 small. And given everything else, i can't see it ever even being the case. That would only happen if Earth was 100% rigid, and i was only force happening at that time.

 

[alkaspeltzar]

If it did matter, then you would have to take into account everything happening around the world: everyone driving, walking, jumping in all different directions.

From a non technical standpoint, that makes a lot of sense. I don't know how you would include everything. And from what i am reading, everything all over the world also happens to cancel everything out. So these effects IF ANY, can always be ignored unless we are talking about Planet size forces and such

 

[PeroK]

From a non technical standpoint, that makes a lot of sense. I don't know how you would include everything. And from what i am reading, everything all over the world also happens to cancel everything out. So these effects IF ANY, can always be ignored unless we are talking about Planet size forces and such

Or, the tides caused by the orbit of the Moon. That has a measurable effect.

 

[russ_watters]

i did a calc...based on force applied to the Earth based on force applied to 100kg block via gravity. Yeah values 10^-24 small. And given everything else, i can't see it ever even being the case. That would only happen if Earth was 100% rigid, and i was only force happening at that time.

Even for the moon, the barycenter (which the Earth wobbles around) is only about 1% of the distance between the Earth and moon. Still pretty small.

From a non technical standpoint, that makes a lot of sense. I don't know how you would include everything. And from what i am reading, everything all over the world also happens to cancel everything out. So these effects IF ANY, can always be ignored unless we are talking about Planet size forces and such

If you're referring to the cumulative effects of motions on Earth, note that most start and end stationary on the surface of the Earth and an awful lot even start and end in the same place. So their net effects largely even cancel themselves out.

 

[ZapperZ]

According to N3L, every time we move or apply forces, there is a reaction. Therefore, walking, driving and stopping would all affect Earth right?

Then why don't we have to consider that in our physics problems? Wouldn't falling down to Earth's surface mean Earth was moving towards us too, so wouldn't the force be different than if we just fell onto an immovable object?

I know Earth is big, but still it wouldn't it matter? I know this is elementary, but i has my brain questioning and wondering. So insight would be appreciated.

Why stop there? Why not include the gravitatioinal forces from all the celestial bodies in the universe? After all, they are all there, aren't they?

At some point, the decimal places where this actually occurs is so far down the line, will it matter anymore? Have you noticed the effect of the gravity from alpha centauri in your daily lives? Are you pulled to the side when a truck passes by in front of your house?

This is why I always recommend students, even at elementary schools, do "experiments". Because there is something to be said about "realistic" situations and what it means. People need to learn why reading all 12 digits off a number spewed by a calculator makes as much sense as telling someone that the distance between New York City and Chicago is 790.5`1221554538823 miles.

Zz.

 

[Janus]

From a non technical standpoint, that makes a lot of sense. I don't know how you would include everything. And from what i am reading, everything all over the world also happens to cancel everything out. So these effects IF ANY, can always be ignored unless we are talking about Planet size forces and such

Another thing to consider is how large the difference in the answer would be when taking into account all these other effects when compared to the uncertainty of your initial conditions.
So for example, to find the fall-time for a 100 kg object over a given height, you need to know the gravitational parameter(Gm) for the Earth. But our best value for this is only good to 10 significant digits. The acceleration the Earth has towards the block is 1.667e-23 of that the block has towards the Earth. Thus the uncertainty of the value for Gm is much, much larger than the difference in answers between considering the Earth's acceleration and ignoring it.

 

[kuruman]

If the entire population of the Earth were all standing at a single location and jumped up together with an initial speed of 5 m/s, the Earth would acquire a recoil speed of order 10^-13m/s. That's assuming an average mass of 50 kg (110 lbs) per person. The motion of the Earth is quite unperturbed by our antics.

 

[alkaspeltzar]

I guess the question in my head is this:

Say i was walking (2 m/s) and collide with a wall. There is a certain force required to bring me to a stop. But if Earth was actually moving toward me prior to the collision, even if super small velocity like 10^-23, wouldn't that change the force i feel?

I wish i could put numbers to it but i start getting confused.

 

[ZapperZ]

I guess the question in my head is this:

Say i was walking (2 m/s) and collide with a wall. There is a certain force required to bring me to a stop. But if Earth was actually moving toward me prior to the collision, even if super small velocity like 10^-23, wouldn't that change the force i feel?

I wish i could put numbers to it but i start getting confused.

You hitting the Earth at 2 m/s or the Earth hitting you at 2 m/s has no difference.

Zz.

 

[alkaspeltzar]

You hitting the Earth at 2 m/s or the Earth hitting you at 2 m/s has no difference.

Zz.

But the Earth is moving at me too? How is that not different.

What if two equal masses collided. One at V and other at -2V. Wouldnt the magnitude of the force be different compared to both hitting at equal but opposite velocity?

 

[ZapperZ]

But the Earth is moving at me too? How is that not different.

What if two equal masses collided. One at V and other at -2V. Wouldnt the magnitude of the force be different compared to both hitting at equal but opposite velocity?

The relative velocity is what matters. If one is v and the other is -2v, then the relative velocity is 3v. It is no different if you hit the Earth at 3v.

Zz.

 

[jbriggs444]

790.5`1221554538823

Per Ben Affleck in "The Accountant", people making up numbers have an unconscious propensity to use 3's.

[Then too, humans have a propensity to see patterns where none exist]

 

[ZapperZ]

Per Ben Affleck in "The Accountant", people making up numbers have an unconscious propensity to use 3's.

[Then too, humans have a propensity to see patterns where none exist]

I used more 2's and 5's in there than I used 3's. That hypothesis has just been falsified.

Zz.

 

[alkaspeltzar]

Okay but didn't mythbusters show hitting a wall at V and hitting another car at -V were the same.

So a car at V hitting a car at -V is the same as hitting it at V, not 2V.

 

[jbriggs444]

What if two equal masses collided. One at V and other at -2V. Wouldnt the magnitude of the force be different compared to both hitting at equal but opposite velocity?

A +v car and a -2v car colliding would be the same as a +1.5v and a -1.5v car colliding. Which would, in turn, be the same as a +3v car hitting a parked car.

Okay but didn't mythbusters show hitting a wall at V and hitting another car at -V were the same.

A +v car and a -2v car colliding would be the same as a +1.5v car hitting a rigid and stationary earth. Or a -1.5v rigid Earth hitting a stationary car.

 

[Dale]

Okay but didn't mythbusters show hitting a wall at V and hitting another car at -V were the same.

So a car at V hitting a car at -V is the same as hitting it at V, not 2V.

Hitting a wall vs hitting another car is a completely different scenario. It is not the same scenario from a different frame

 

[alkaspeltzar]

Okay I knew I had made a mistake. Back to my original question then, that's why Earth's movement,if any doesn't matter.

Say I am traveling at V and hit a wall. Even if Earth has some micro velocity in the other direction, such at the wall was coming at me, it would be like hitting a wall at V + (something on order of 10^-22). With everything else going on, errors in rounding, measurement, that can safely be ignored.

Correct?

 

[Nugatory]

Okay but didn't mythbusters show hitting a wall at V and hitting another car at -V were the same.

So a car at V hitting a car at -V is the same as hitting it at V, not 2V.

Car on car is a different problem than car on solid wall.

Say that when a car hits a solid object at speed $v$ meters/sec, its nose is crushed back by $x$ centimeters. That means that its speed goes from $v$ to 0 in the time that it takes the car to travel distance $x$; we can calculate the force required to do that. (Try it - it’s fun! Assume constant deceleration so the average speed of the car while it crumples and comes to a stop is $v/2$; that will tell you how much time the collision takes, from that you can calculate the acceleration and $F=ma$ will get you home from there).

But in a car to car collision you have twice the crumple distance. Run through the same math and you will find that car on wall at closing speed $v$ is the same as car on car at closing speed $2v$. Two cars both moving at $v$ and colliding head on is the same as hitting a parked car at $2v$ or a solid wall at $v$

 

[jbriggs444]

Say I am traveling at V and hit a wall. Even if Earth has some micro velocity in the other direction, such at the wall was coming at me, it would be like hitting a wall at V + (something on order of 10^-22). With everything else going on, errors in rounding, measurement, that can safely be ignored.

The difference between hitting a wall that is infinitely rigid and infinitely massive and hitting a wall that is infinitely rigid and attached only to a finitely massive Earth is likely on the order of 10^-22.

The difference between hitting a wall that is not nailed to the foundation, to the other walls or to the ceiling and hitting a wall that is tied in -- that could range up to 50 percent.

 

[sophiecentaur]

But in a car to car collision you have twice the crumple distance.

[Edit I assume the cars are traveling towards each other at equal speeds]
The bumpers (fenders?) of both cars will ideally be at the mid point of their centres of mass at all times during the collision. So each car will be doing work on its own crumple zone as the cars come to a halt. Replace the front of one of the cars with a solid wall and there is no way that the moving car would know the difference. Its crumple zone would end up with the same amount of crumple because exactly the same work was done to dissipate its KE.