A compressed spring contains more energy than an uncompressed one. To balance the equation mass must increase, although EXTREMELY little, because c is constant.

Weight is mass x gravity so a higher mass equals a higher weight.

A compressed spring may be `denser` than an uncompressed one, but they weigh the same... Actually, the compressed spring contains energy. That energy has an equivalent mass m = E/c^2, which is quite small but still greater than zero.

@HG & @OO I heard something... in stereo! (stereo!)

(get it? My wordplay of the day!)

I was about to agree, but then I thought: there`s 3 ways to "store energy" - mass - heat - kinetic

Doesn`t the compression of the spring simply ADD kinetic energy? As @stk5m wisely points out: not one single atom of mass is gained... electron even!

The E=Mc^2 is a simplification which requires OTHER variables (like momentum for example, which is a form of... kinetic energy!) to be constant too. Or zero...

Fun facts. Number 5 is a little off base however. If the book took 45 minutes to `fall` to the centre of the Earth, it would have to be travelling at an average of approximately 5200 miles per hour, which would be impossible. In reality it would take a huge amount of time to fall, as the closer you get to the centre of the Earth, the smaller gravity becomes until you reach the centre where it is zero. The book (or any object) will therefore continue to slow due to air resistance all the way to the centre. It would take an inordinately long time for any object to fall to the centre.

wibble4321, you got it wrong, it would not take that long, in fact, it would still increase in speed until it reached the center, just this increase would be lower and lower the closer to the center it is. On the earths surface an object drops with around 10 meters/sÂ². As it reaches more and more depth, the part of the earth that it has passed starts pulling more and more on it, reducing the rate in which the speed of the item increases, but it will only ever start slowing down when the book reaches the center of gravity (and would continue to fall to the other side of the earth). Think of it like a linear pendulum

Corydoras, sorry, no. As it sinks below the surface of the earth there is increasingly mass above it. The mass of the earth above the book begins to apply an increasingly strong gravitational pull in the opposite direction. At the centre of the earth there is no gravity (caused by the Earth) because the mass of the Earth is evenly distributed all around the centre pulling equally. Gravity is not a single localised `thing` an object doesn`t have one spot where gravity exists - gravitational pull is exerted by everything that has mass.

Re-reading your text I wonder if you have not taken into account terminal velocity? The book has a drag coefficient that slows it - it cannot reach that speed. It will initially accelerate a 9.81m/s2 until the drag overcomes the acceleration.

A very quick calculation sets the random fact to be quite off.

The average radius of Earth is about 6371 km. Assuming the terminal velocity of a book is ~200km/hour the same as any given Object without effecient friction reducing facilities.

6370000m/200000m/hr = 31.9hr =1.3 days

Assumptions: 15 Seconds to Reach terminal velocity not taken into consideration but this would add time not reduce. Variance in air friction not taken into consideration but this would likely slow it Down further.

The growing mass that it has passed, and the gravitational pull that it would cause, would likely be miniscule as the main pull comes from the dense inner core. Its very likely that it would have an effect on the books velocity but unlikely that it would actually change the result greatly.. much less change it to 45minutes.

You all need to reread the fact, it says; "if you dig a hole to the center of the Earth", OK, so now you are at the center of the Earth, it will now take that book 45 min to fall to your feet.

In reference to the moon/ocean floor thing... that`s why it bugs me when I hear that space is `the final frontier` (despite being a Star Trek fan) ... nope, we still haven`t fully explored the oceans yet. AFTER that it`s space.

"Lets think bigger: if you dug a hole to the center of the Earth and dropped a book Down, it would take 45 mins to Reach the bottom:"

Well if you want to be technical, its not stated where exactly this bottom is. The gravitational pull also varies depending on Your distance from the Source. So even if we were at the bottom of this hole, its unlikely that it would take 45 minutes as the gravitational pull would be greater than on the surface.

I`m pretty sure you couldn`t actually dig a hole to the center of the earth. I think at some point, long before you reached the center, the pressure would be so great that you simply could not keep any kind of hole open no matter what materials or engineering design you used.

@Gerry1of1: to simplify what @pazerlenis said, because the spring has more potential energy from the force of compression, it makes the mass increases and therefore the weight does as well. It would work the same way if you threw the spring at someone, it would weigh more than if it was still. Or if you said a hot spring weighs more than a cold spring, obviously because hot springs are big.

@Lednar - it depends on whether you`re using the long scale or short scale. Either one is correct, it`s dependent upon the scale being used. Using the short scale, your version of one trillion is called a quintillion.

Get your facts straight and shove the `murica bullpoo up your wanker ass.

I think (but have not looked it up) that when you compress the spring you change it`s DENSITY: the same mass is now in a (slightly) smaller volume. I mean the walls of the spring itself get smaller, not just the spring "getting shorter" eh? More density = greater distortion in the space/time field which affects... the speed of light! After all, it`s not a "constant" it`s subject to various variables, including dents in the fabric of space-time. Again, it`s literally impossible to measure as it is such a TINY number.

Just like when you move a 10 pound weight you`ve moved the Moon. You can calculate it... but never measure anything THAT small! Not to mention 1,000 other unknown variables...

The falling book thing should have read: "bla bla bla.. (assuming a perfect vacuum)".. In a perfect vacuum, it`s about 42 minutes to fall through the earth to the other side, only by the influence of gravity. Drag messes up all the beautiful math. Stop ruining the cool physics !..

5Cats: The entire theory of relativity is based on the assumption that the speed of light in a vacuum is a universal constant, and does not depend at all on how you`re moving through the universe, or what kind of field you`re in. So no, the speed of light doesn`t change.. therefore, the mass must.

If you compress a spring, you add potential energy to it by distorting the molecular bonds away from their ground state. when you release it, it jumps up, because the molecular bonds go back into their original configuration. This stored potential energy is still real energy, and still factors into the E = m*c^2 equation..

@Kain1 Nope! Not trolling. In a vacuum, yes. BUT light is affected by gravity. And gravity is affected by density. And the speed light travels at does vary according to the medium (usually a vacuum of course).

My problem with the "gains mass" idea is that this would require easily changing energy into matter and then BACK, easily! Bzzt!

I think it`s easier to change the speed of light (via density) than to convert mass & energy around. Just like I can "move the moon" eh?

The Energy increases, the Mass stays the same so the Speed of Light (squared) is INCREASED to keep it balanced...

I did get it "arse backwards" in my explanation below, it <increases> due to more density (gravitic effects). SPEEDS UP in a "relative way" eh? Again, it`s such a tiny number it`s incomprehensibly small!

- Fact: Shrute Farms is on Google. How`s that for random?
No, I`m not looking it up! Lazybones...

E=MC2

A compressed spring contains more energy than an uncompressed one. To balance the equation mass must increase, although EXTREMELY little, because c is constant.

Weight is mass x gravity so a higher mass equals a higher weight.

Actually, the compressed spring contains energy. That energy has an equivalent mass m = E/c^2, which is quite small but still greater than zero.

What? You didn`t like my explanation? ;)

I heard something... in stereo! (stereo!)

(get it? My wordplay of the day!)

I was about to agree, but then I thought: there`s 3 ways to "store energy"

- mass

- heat

- kinetic

Doesn`t the compression of the spring simply ADD kinetic energy? As @stk5m wisely points out: not one single atom of mass is gained... electron even!

The E=Mc^2 is a simplification which requires OTHER variables (like momentum for example, which is a form of... kinetic energy!) to be constant too. Or zero...

It was on IAB before!!! (lolz!)

Re-reading your text I wonder if you have not taken into account terminal velocity? The book has a drag coefficient that slows it - it cannot reach that speed. It will initially accelerate a 9.81m/s2 until the drag overcomes the acceleration.

A very quick calculation sets the random fact to be quite off.

The average radius of Earth is about 6371 km.

Assuming the terminal velocity of a book is ~200km/hour the same as any given Object without effecient friction reducing facilities.

6370000m/200000m/hr = 31.9hr =1.3 days

Assumptions: 15 Seconds to Reach terminal velocity not taken into consideration but this would add time not reduce.

Variance in air friction not taken into consideration but this would likely slow it Down further.

that`s why it bugs me when I hear that space is `the final frontier` (despite being a Star Trek fan) ... nope, we still haven`t fully explored the oceans yet. AFTER that it`s space.

"Lets think bigger: if you dug a hole to the center of the Earth and dropped a book Down, it would take 45 mins to Reach the bottom:"

Well if you want to be technical, its not stated where exactly this bottom is.

The gravitational pull also varies depending on Your distance from the Source.

So even if we were at the bottom of this hole, its unlikely that it would take 45 minutes as the gravitational pull would be greater than on the surface.

How can a spring weigh more when compressed.

You`re not counting the weight compressing it, just the spring itself. ... I don`t recon that one.

A compressed spring does have a bit more mass due to stored energy. HOWEVER. the amount is so small you could never measure it.

Say: 1000 J = 1000 kg*m^2/s^2

E = Mc^2

1000 = M * (3 * 10^8)^2

10^3 = m * 9 * 10^16

M = 1 * 10^3/9* 10^16 = 0.11 * 10^-13 kg = 0.00000000000001 kg

I did not just copy/paste that from yahoo answers...

and one trillion = 1.000.000.000.000.000.000

Sometimes I think `muricans use those words because they just sound fancy.

Get your facts straight and shove the `murica bullpoo up your wanker ass.

More density = greater distortion in the space/time field which affects... the speed of light! After all, it`s not a "constant" it`s subject to various variables, including dents in the fabric of space-time.

Again, it`s literally impossible to measure as it is such a TINY number.

Just like when you move a 10 pound weight you`ve moved the Moon. You can calculate it... but never measure anything THAT small! Not to mention 1,000 other unknown variables...

The Energy increases, the Mass stays the same so the Speed of Light (squared) is reduced to keep it balanced...

The higher density alters the fabric of space/time which slows light (in that RELATIVE way, eh?).

"bla bla bla.. (assuming a perfect vacuum)"..

In a perfect vacuum, it`s about 42 minutes to fall through the earth to the other side, only by the influence of gravity. Drag messes up all the beautiful math. Stop ruining the cool physics !..

5Cats: The entire theory of relativity is based on the assumption that the speed of light in a vacuum is a universal constant, and does not depend at all on how you`re moving through the universe, or what kind of field you`re in. So no, the speed of light doesn`t change.. therefore, the mass must.

If you compress a spring, you add potential energy to it by distorting the molecular bonds away from their ground state. when you release it, it jumps up, because the molecular bonds go back into their original configuration. This stored potential energy is still real energy, and still factors into the E = m*c^2 equation..

In a vacuum, yes. BUT light is affected by gravity. And gravity is affected by density. And the speed light travels at does vary according to the medium (usually a vacuum of course).

My problem with the "gains mass" idea is that this would require easily changing energy into matter and then BACK, easily! Bzzt!

I think it`s easier to change the speed of light (via density) than to convert mass & energy around. Just like I can "move the moon" eh?

The Energy increases, the Mass stays the same so the Speed of Light (squared) is INCREASED to keep it balanced...

I did get it "arse backwards" in my explanation below, it <increases> due to more density (gravitic effects). SPEEDS UP in a "relative way" eh?

Again, it`s such a tiny number it`s incomprehensibly small!