Ask a physicist anything. (8)

[Wiccan_Child]

That was the conundrum. If matter (3 dimensions) exists in time (the fourth) then there should be some way of measuring it in relation to the other three.

How do you mean?

 

[Jonathan Jarvis]

MOD HAT

Sorry - had to do a bit of clean up. There was some inappropriate discussion going on .

Sorry to bother you. Not sure how Mod Hat works. Is the postings that you are refering to mine and Wiccan's about linear time or other posts that have been removed?

 

[AV1611VET]

Is the postings that you are refering to mine and Wiccan's about linear time...

No.

... or other posts that have been removed?

Other posts -- you're fine.

 

[Wiccan_Child]

Sorry to bother you. Not sure how Mod Hat works. Is the postings that you are refering to mine and Wiccan's about linear time or other posts that have been removed?

Something tells me it was the talk about wet t-shirt contests.

 

[super animator]

nm.

 

[Cactus Jack]

Three questions-
1. What is the deepest mine in the world?
2. What is the deepest well drilled in the world?
3. And what is the probability of man either drilling a well or driving a tunnel to the other side of the Earth? And why?

 

[Wiccan_Child]

Three questions-
1. What is the deepest mine in the world?
2. What is the deepest well drilled in the world?
3. And what is the probability of man either drilling a well or driving a tunnel to the other side of the Earth? And why?

Phenomenally unlikely, even in the far future, as there's little benefit and supreme difficulty in tunnelling through the mantle.

Interestingly, it would take 42 minutes (source) to fall from one part of the Earth to the other, no matter what angle your line moves, whether it's this:

Or this:

 

[QueSi]

Phenomenally unlikely, even in the far future, as there's little benefit and supreme difficulty in tunnelling through the mantle.

Interestingly, it would take 42 minutes (source) to fall from one part of the Earth to the other, no matter what angle your line moves, whether it's this:

Or this:

Can someone fall through the second picture? Wouldn't they be pulled more towards the larger mass of earth?

 

[essentialsaltes]

Can someone fall through the second picture? Wouldn't they be pulled more towards the larger mass of earth?

True. But some people (more in jest than seriousness) have proposed putting airtight railcars in such a tunnel, sucking all the air out (to eliminate wind resistance) and using it for quick transport. Cars would roll faster and faster 'downhill' during the first half of the trip, and then slow down during the 'uphill' section. If you could totally eliminate friction and air resistance, it would cost no energy to do this, and the car would come to a stop just as it reached the exit.

As Wiccan Child noted, such a tunnel would be practically impossible to dig, due to the earth getting hotter and liquidier down there.

 

[Wiccan_Child]

Can someone fall through the second picture? Wouldn't they be pulled more towards the larger mass of earth?

From the entrance, it'd look like a tunnel going into the Earth at an angle. If you laid tracks along it and rode it like a straight rollercoaster, gravity would do all the work because you're going downhill. Counter-intuitively, though the slope never changes, gravity changes such that you end up going at a shallower and shallower decline, until you're going level, and then uphill. Gravity would ensure you'd have enough speed to make it just far uphill enough to reach the lip of the other side.

But you're right, a man couldn't 'fall' though if the angle is far off from straight down. Trains could do it, though.

 

[super animator]

theoracticly speak if you drill a hole to one end of earth to another and drop the ball, will it bounce up and down forever assuming there is no collention happen and air Resistance say the same?

 

[Wiccan_Child]

theoracticly speak if you drill a hole to one end of earth to another and drop the ball, will it bounce up and down forever assuming there is no collention happen and air Resistance say the same?

Yep. It wouldn't 'bounce', though, as that implies it rebounds off of something. Instead, it would speed up as it fell towards the centre of the Earth. But gravity decreases towards the centre, so though it's speeding up, it accelerates less and less.

At the centre, there's no acceleration. As it passes through the centre, gravity now begins to work against the ball's motion. Gravity increases as the ball soars 'up' through the tunnel towards the exit, and the ball slows to a halt just at the lip of the exit - and then falls back down, repeating the process.

Disregarding air resistance, this process is a simple harmonic oscillator.

 

[Davian]

Yep. It wouldn't 'bounce', though, as that implies it rebounds off of something. Instead, it would speed up as it fell towards the centre of the Earth. But gravity decreases towards the centre, so though it's speeding up, it accelerates less and less.

At the centre, there's no acceleration. As it passes through the centre, gravity now begins to work against the ball's motion. Gravity increases as the ball soars 'up' through the tunnel towards the exit, and the ball slows to a halt just at the lip of the exit - and then falls back down, repeating the process.

Disregarding air resistance, this process is a simple harmonic oscillator.

Would not you have an issue with the ball hitting the sides of the hole, due to the Earth's rotation, unless the hole was located at the axis of rotation?

 

[Loudmouth]

Would not you have an issue with the ball hitting the sides of the hole, due to the Earth's rotation, unless the hole was located at the axis of rotation?

Yep. I believe the major problem is the differential speed of rotation as you go deeper underground being that the outside of the Earth is moving at a much higher speed than a few hundred feet out from the core.

 

[super animator]

Would not you have an issue with the ball hitting the sides of the hole, due to the Earth's rotation, unless the hole was located at the axis of rotation?

If the earth rotation is a constant angler velocity then it shouldn't hit the sides of the hole. Now in real life, this isn't necessarily true, but the changes to the rotation is so small that you hardly notice any changes to it. I would say very very very unlikely.

(Studying physics in college.)

 

[essentialsaltes]

Yep. I believe the major problem is the differential speed of rotation as you go deeper underground being that the outside of the Earth is moving at a much higher speed than a few hundred feet out from the core.

Yes, this is essentially the same as the Coriolis Effect.

 

[Loudmouth]

If the earth rotation is a constant angler velocity then it shouldn't hit the sides of the hole. Now in real life, this isn't necessarily true, but the changes to the rotation is so small that you hardly notice any changes to it. I would say very very very unlikely.

(Studying physics in college.)

If someone has the time and the interest, they could go to a local playground that has a merry-go-round and roll a marble or ball from the outside towards the inside and see if its path strays to one side or the other if it is spinning.

 

[Davian]

If someone has the time and the interest, they could go to a local playground that has a merry-go-round and roll a marble or ball from the outside towards the inside and see if its path strays to one side or the other if it is spinning.

I was thinking more along the lines of a Foucault pendulum:

Foucault pendulum demonstrating the Earth's rotation - YouTube

 

[Strathos]

I've got one: How would you calculate the speed of an object falling through water? For example, say you dropped a rock into a pond, and it took 10 seconds to hit the bottom. How deep would that mean the water was?

 

[essentialsaltes]

I've got one: How would you calculate the speed of an object falling through water? For example, say you dropped a rock into a pond, and it took 10 seconds to hit the bottom. How deep would that mean the water was?

Pragmatically, there are probably easier ways to measure the depth of a pool.

Getting directly to the question, it would depend on the shape and size of the rock in a complicated way.

Operationally, the fluid resistance is often modeled as a force proportional to the speed of the object as -bv. With an empirically measured value of b, one could calculate the depth of the pool based on the time of falling.