Force of gravity?
 

Ok, so call me a freak but I was going up the escalator in a station this morn & i started thinking about gravity. It seems logical (to me) that climbing a moving stairs is more difficult than a static stairs - coz youre actually tarvelling faster/farther than you would on a nonmoving. SO,
1. Does the force of gravity increase when youre travelling upwards?
2. If im travelling straight up, how fast do I need to be going to double the force of gravity?
3. And at 45 degrees?
4. If im travelling on a train/lift/whatever at the speed of sound (Mach 1) and I start running towards the front of the train how fast am I travelling & is the force of gravity on me different to the force on said vehicle?

The force of gravity is determined by your mass, the earth's mass, and the distance between the center of those two masses.

Your velocity does not affect the force of gravity. The fact that you may experiencing acceleration do to other forces, does not mean that the force of gravity has changed. The acceleration due to gravity is 32 feet per second per second. You would have to add a force that would cause the same acceleration in the same direction to cause the sensation of doubling the force of gravity. Keep in mind that force = mass x acceleration. So your mass would have to be known to calculate the force that would do this. When another force is applied at 45 degrees to perpendicular, exactly on half of the force would be added to gravity. The other half would be the horizontal component.

I don't remember the exact formulas, but there is a dusty thought in the back of my brain that the force of gravity is inversley proportional to the square of the distance. This would mean that you would have to dig down 3/4 of the way to the center of the earth to experience a doubling in gravity. Of course you could just apply weights, as that would be easier, and a whole lot cooler.

Hold on everyone -- Rogue will be by in a few minutes...

This just sailed way over my head... Boobs anyone?

Gravity is assumed to act from the centre of the planet so digging down wouldn't effect it in the wya of equations but thinking logically it should have some effect on it.

If you going upwards at a constant speed you'l notice no differences from gravity (unless your travelling so fast that the earth is no longer effecting you) [again i say you'll not notice, if say you were an atomic clock instead of an TFP poster you might notice there's a change in g at altitude].

As you go upwards you are gaining potential energy faster BUT the floor is going up and that's providing the power.

if you were accelaerating upwards at 9.9081 m/s^2 your weight would be twice as much (although your mass is constant).

If travelling at 45 degrees upwards you'd need to accelating at root (9.9801^2 + 9.9801^2) which is 14.11m/s^2.

The gravity constants are from my head so may be wrong but are in the right ball park for figures. Hope this helps somewhatt.

I always liked to imagine a hole through the centre of the earth that you could jump through and experience simple harmonic motion, but then again I don't get to sleep alot and have time on my hands! Hope this helped.

Insom

The force of gravity by classical physics (which are good enough for this discussion) can be calculated as

F = G * (m1 * m2) / r^3, where F is the force we're looking for, G is the gravitational constant, m1 and m2 are the two masses in question, and r is the distance between the two.

So, answering your questions:
1. because the force is inversely proportional to the cube of the distance, gravity actually decreases as you go away from Earth.

2. Well, you can put another force on yourself, double that of gravity. I won't go into that, though, as I doubt that's what you're talking about.

3. the "angle" won't make a difference, the distance between the two bodies will.

4. You'd be travelling at a speed of however fast you were running plus the speed of the train. As I assume the train is on the Earth, then the distance between you and Earth's center of mass won't change, so gravity will remain constant.
Gravity will be ever so slightly stronger on the train because it has more mass than you; however, the difference is neglible. Gravity is a force at work on astronomically large bodies, on smaller bodies it is far too weak.

Ouch, my head hurts!!!

In $1 words (I hope):

First of all, walking on an escalator is not harder than walking on stairs, because your speed <i>relative to</i> the two is the same.

1. The force of gravity always remains constant, regardless of the direction you are traveling. Sometimes it works in your favor (going down), sometimes not (going up). But it never changes.
2. You cannot realistically double the force of gravity, however, if you were accelerating UP at 32' per second squared, you would experience the <i>feeling</i> of double that of normal gravity.
3. At 45 degrees, it's still pulling you down at 32' per second squared. it's easier to walk at 45 degrees compared to straight up because for every foot uphill you walk, you also walk a foot horizontally. However, in order to travel the same distance vertically, walking at 45 degrees requires you to walk twice as far (total distance) That's the give-and-take. Think of using a board as a ramp up to something - the more gentle the slope, the longer the board you'll need, and the more steps you'll need to take to reach your destination.
4. If you are traveling on a train and start running, your speed is the sum of the train's speed plus your speed (or <i>minus</i> your speed - if you run from front to back). The force of gravity is still constant.

As <b>greytone</b> accurately pointed out, the <i>actual</i> force of gravity is 32 feet per second per second (or 9.8 meters per second per second)<i>at sea level</i> (and at the equator, I think). Naturally, this force actually changes relative to your distance to the center of the earth. However, for all practical purposes, I think it's safe to assume it's a constant. Most of us will never vary that distance by more than 8 miles or so, and considering the distance to the center of the earth is close to 15,000 miles, that's not much of a difference.

There - that's not as accurate or eloquent as <b>greytone</b> put it, but I hope it helps clarify some things.

*Escalator= Moving stairs.

Urm, consider your relative velocity wrt to the moving escalator* when you are standing on it still. Zero. When you move, you exert about as much force as you would on a "normal" staircase of identical charecteristics.Therefore to answer you pointwise:

1. Gravitational force decrease with distance.

Consider g aka acceleration due to gravity. It depends upon mass(kg) of Earth(M) and the radius(R)(unit is meter) of the planet and the formula is g=((MG)/R^(2))=~9.8m/s^(2) roughly. G is the universal constant of Gravity and its value is 6.67*10^(-11) Nm^(2)kg^(-2)

Therefore the gravitational force(F) has unit Newton and is calculated by the formula F=mg where m(small) is the mass(kg) of the object(you) and g the acceleration due to gravity.

Note that the g is independent of the mass of the object. Of course, the object(you) also exert gravitational force on the Earth but considering the difference in the scale it's negligible and can be safely ignored. Or don't ignore it. Whatever floats your boat.

Work is defined as Force*Distance and the units is Joule so the actual work you'll be doing in this case would be (mg)(h2-h1) where hn is your difference in initial and final height, m is your mass and g the acceleration due to gravity. Now....the value of g decreases with increase in R, so actually you'll be doing less work when climbing the same distance on a already high situated escalator rather than a "ground level" staricase. But all this is codswallop because the difference in R is negligible, nor is the centre of mass properly defined.

TO the point, there is this thing called power[unit Watt]. Power=Work/Time. Therefore, the power exerted by you would be more if you are trying to cover the same distance(vertical component, obviously) in shorter period of time. May be you try to climb faster while on escalators? I know I do. All things equal, escalators will help conserve your fat more than the regular stairs. If only because you'll be covering the same distance in shorter time. So take the "static" stairs and stay healthy.



2. Double the force of Gravity? And that too while going straight up?! Gravitational Force between two mass bodies is calculated with F= ((GMm)/R^(2)). And since you are already going up and increasing the distance, and since you cannot possibly influence the Mass(M) of the Earth, and G is G, what we can do is increase your mass dramatically, all the while ensuring that as you go up more mass is addded! Maybe we could teleport lots of Ice-cream to you...

Haha, I am so funny.http://www.atlasf1.com/bb/images/smilies/rolleyes.gif

In case you were trying to refer to acceleration due to gravity aka g as experienced by your body, while travelling vertically, all you would have to do is build an apparatus like a rocket/plane that can provide you with 2g acceleration vertical. The initial speed would be zero, obviously, and after that it would keep increasing wrt time. So either with known rate of acceleration we can calculate speed at t seconds after launch/take-off, or if you want x speed at y distance than we can calculate the rate of acceleration. This is dealing purely with vertical component ie 2d.



3. You haven't specified in what axis you want to feel this 2g force. If it's the net of the horizontal and vertical in 3d, then it can be easily calculated through trignometric formula though because of my lame HTML skills I cannot elaborate more here. However, you can easily experience this much g's on Earth surface itself 2d. Any car that brakes from 100 kmph to 0 within 1.4 seconds. F1 cars with carbon-fibre brakes regularly hit more g's(momentarily, and decreasing) at the end of long straights followed by slow corners.



4. Relative velocity. And depends on the point of observation. As a point object, and certainly if mass is taken into consideration, all your running stunts are pretty much ignorable and "your" speed will be taken as the speed of train(x kmph). Relatively, however, your body is at rest (inertia) and if you start running(y kmph) towards front you will momentarily be covering more distance per unit time(x+y kmph) compared to other pax(x kmph) and are "faster"(by y kmph) than the train, to someone viewing this whole scene from a staionary platform from the outside. That is, until you run out of room and head back to your seat. So you'll arrive at the same time as the rest of the pax.


Gravity, as you know by now, applies to mass. For all theorotical physics problems, we take a point mass(hypothetical), where all the mass of an object is centered, and then calculate. So, your mass is irrelevant, what matters is the total mass and how it's distributed to make sense from an engineering point of view. Because you are travelling at the same speed as your vehicle, your and your vehicle's mass is combined in calculations. But as soon as you jump out, you'll be taken as a seperate point mass and studied as you form a nice trajectory and come to rest. Strictly, the force of gravity is affected only by the variables mentioned in te formula. Draw your conclusions.


EDIT: Improved Formatting. Relatively speaking.

You don't say so
 

In civilized world, it is called 9.8 meters per second:p ;)

Re: You don't say so
 

Not to split hairs, <b>oane</b>, but 9.8 meters per second would be a velocity.

9.8 meters per second <b>squared</b> is acceleration.

I know you meant that.

Re: Re: You don't say so
 

Damn!:o Yeah, you are right...heh.

I know he will, I was just trying to beat him to it for once.

As for the units, I just could not remember the value in m/s/s. I knew it was 9 point something, but I had not used it in many years. I think in metric at work (except temperature and usually body weight) and the old English system at play.

I think I actually understand this now! I've been wondering about that train problem, too. Thank you, tfp.

In layman's terms.......gravity sucks

"escalators are great because they won't break down... they just become stairs"
-- Mitch Hedburg (Comedian)

Heres something i always wondered about gravity... if you have a hole that goes straight through the planet, much like when you core an apple... and you jump into this hole. Do you get stuck in the center of the planet? Do you get ripped to shreds? all this is assuming that the immense heat does not effect you.

That's a pretty dangerous assumption.

But - and please correct me if I'm wrong (Ha - like no one would!), I believe that, also assuming you don't bump up against the sides of the holes, and neglecting air friction (and air pressure), you would appear at the opposite end of the hole (upside down, of course), with the top of your head at ground level, then start your descent again, where you would appear again at your point of origin - feet at ground level. But of course, although Physics 101 may let us neglect air friction, the real world doesn't, so each "ascent" up the hole from the center would get shorter, and yes, eventually, your body would be stuck at the earth's center, burnt and compressed into a tiny, unrecognizable, dense cinder.

Of course - that's all theory - if you've got the shovel and the time, go for it.

You know, it's nice to see some people paid attention in physics. I know I didn't. Way too much time spent talking and making bad jokes. Oh well, I did ok and it was a damn good time.

Nah, I think you all pretty much got the info down.

Now, here's the REAL question.

WHY does gravity act that way?


BTW, besides all your explanations of gravity.
You forgot to say to the questioner why they are "feeling"
a change in "pull".:)

The change you might "feel" when you are going faster (accelerating),
or going slower (decelerating)
is because you are changing your velocity in respect to the laws of inertia.

This means as you go faster, you "feel" a pull.
And as you go slower, you "feel" a push.
And this "feeling" can exist when you change your direction too.

This is why you are "feeling" pushed & pulled all different types of ways on a roller coaster.
It's not gravity changing, the pull is always constant (at least on that small scale)
Gravity only affects the energy or work needed to move you back up, but the coaster is taking care of this.
Notice that on your ride the hills are getting smaller and smaller.
That's because of the loss of energy through friction,
it doesn't have as much to get up the next hill.

However, let's say you were on the same roller coaster,
but now it's up on the non-gravity space-station and the first car is pulling at a constant rate.
Even though there is no gravity & no acceleration you would still feel all the twists and turns, etc. that you felt on Earth.
Why?
Because as you change direction you are changing your relation in Space with Inertia.

Some all this "Centrifigal Force"
But this is NOT really a "force"
This is an illusion, an effect.
Because your body wants to continue in a straight line ALWAYS.
But the car you are within is pulling you left & right, etc.
And then you "feel" the pull in the opposing direction.
Giving the illusion of a force or "gravity".

Aww, did I scare everyone away?

Well, someone once said,
"Don't talk physics in public"
;)

"Sorry for the convenience"

:) I love mitch hedburg

All I heard was "LA LA LA LA LA Boobs Anyone?"

In all seriousness, has anyone ever entertained the thought that walking is just a form of controlled falling?

World's King:

Yes please

Urm, I thought this was a known fact that didn't need stating. You are always falling thanks to g.

Re: You don't say so
 

You mean 9.8 meters per second squared. Meters per second is just a velocity. ;-)

Rogue, I think we need to come closer to a unified theory before we can explain "why" gravity does what it does. I personally have no clue. As a Kant fan, I just observe my surroundings and hope they don'tchange laws tomorrow. :-)

must...fight...knowledge....must.....fight....it......AAAAGGGGHHHHH!!!!!!! I'M LEARNING!!!!!!!!!!!!!!!!! NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Re: Re: You don't say so
 

Actually, we don't need to come even close to a unified theory to explain this.

First, gravity is explained pretty much by Einstein's General Theory of Relativity
which states that ANY mass "warps" the Space-Time surrounding it.

Kind of like a bowling ball in the middle of a rubber mat.

And if we pretend "we" are a marble moving at a certain rate near this mat,
we can see the effects of gravity.

If you are moving at a fast enough rate, in comparison of the warping caused by the ball,
then the path will curve and then escape area of the warp.

If you are moving at a constant rate in comparison but not fast enough to escape the area,
the marble will start circling the ball at a certain distance or "orbit"

If you are moving too slowly in comparison,
the marble will curve "fall" to the edge of the ball and come to rest against it.
This is why we stand on the Earth
We are constantly falling toward the middle, but the Earth holds us with its substance.

BTW, by this very definition, I doubt Gravity will ever "fit" into a Unified Theory
with the other 3 forces (Strong, Weak, and Electro-Magnetism)
Because with this significant description we see Gravity is not a force,
it is an effect, an illusionary "force" caused by the warping of Space-Time.
It can be used as a force in certain calculations but it's not actually one.

Thus the Unified Theory as they are now defining it will fail,
Until they change their conceptual viewpoints.

just want to add, strictly physics wise, yes more work is done by you climbing a moving stair, however not by you. By the equation, more work is done because you moved the same distance in less time.

If Nibiru ever comes by again is it possible for the Earth to stop rotating briefly?

I've actually thought about this myself. Very interesting to think about when you don't have much to do! It had kept me busy for hours on end.

Wha?