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4

For a 6 year old, you might want to focus on thickness instead of length, as the numbers get too big with length. A ream of paper (500 sheets) is a bit over an inch thick, say $3.5 \, \text{cm}$, so one sheet is $3.5/50 \, \text{mm}$, or $.07 \, \text{mm}$, which is $7 \times 10^{-5} \text{m}$. An atom has diameter $0.1 \, \text{nm}$ to $0.5 \, \text{nm}$ ...


5

A typical atom is roughly a few times $10^{-10} \text{m}$ wide. A piece of paper is say $(1/4) \text{m}$ wide. Therefore the ratio of the width of an atom to the width of a piece of paper is around $10^9$. A piece of paper is roughly the same width as a human, so $10^9$ is also a rough guess for the ratio of the width of a human to the width of an atom. The ...


-1

It's true that the natural speed limit is the speed of light. So the minimum time required is 1400 yrs. However, it is imposible to reach that speed. We can't even accelerate subatomic particles to that speed. You asked for the fastest rocket in Earth. The actual record of speed is the Helios II spacecraft (obtained from here) which traveled at 70.22 km/s. ...


13

I don't think this sounds unreasonable as an estimate at all. Let's check it. One designs a building as a compromise between two competing factors: One needs all of the load bearing materials to be well mildly loaded - working in their linear region so that there is no danger of their undergoing plastic (irreversible) deformation, creeping then ...


1

Young's modulus is the ratio of tensile stress to tensile strain for a material: E = (F/A)/(∆L/L) = (F * L) / (A * ∆L) F/A is force per area, and (∆L/L) is change in length per original length For structural steel, Young's modulus is 200 gigapascals. This quantity can be used to predict how much the steel will compress under a given weight per unit area. ...


1

Let us make an estimate. Let the skyscraper be 400 m tall, each storey 4 m high, 500 people per storey, 20 m2 per person, 10000 m2 per storey, let us assume that the building is a 100x100 m2 square in the plan and that it only has 10 cm thick structural walls in a 25x25m2 grid. So the cross-section area of the structural walls is 2x5x100x0.1 m2=100 m2. Let ...


1

According to the wiki page the 747 has a max takeoff "weight" of about 350,000 kg (depending on the model) and a wing surface of about 500 m2. That means that a force of 3.5 MN must be carried by 5 million square cm, or 0.7 N per square cm. If you can somehow split this evenly between the top and bottom surface, then you need to come up with a paper surface ...


2

Giving that most of the solar system's mass is concentrated in the sun, you may say that the order of magnitude of the number of atoms in the sun and in the solar system is the same. Thus, we may find this number by using the sun's mass and dividing it by the hydrogen's mass, because the sun is composed of it almost entirely: ...


6

A very brief Google search gets you the number 1,192,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 (approximately $10^{57}$ atoms)- but in fact this is wrong. That value is derived from the mass of the objects of the solar system (mostly the Sun) divided by the mass of a proton (which is what most of the Sun is made of). But the ...


11

anyway, how likely is it the ice ages could be explained by the earth 'realigning' so that polar regions would migrate over the surface of the earth? How about zero? The geological evidence of the Ice Ages clearly says that, between the ice episodes, the ice did not move. It's just that the polar caps shrank. For instance, the extent of the last ice ...


0

If you use a highly simplified model without an atmosphere, it could slow the rotation of the Earth. It would be like riding a ferris-wheel and throwing a piece of popcorn straight ahead as you go around. AKA negligible. Physically speaking the torque created by the rocket, assuming its bolted down well enough, would be the force it exerts times the radius ...


2

The Saturn V threw roughly $m=3\times 10^6{\rm kg}$ out its hinder end at a speed of about $v=3{\rm km\,s^{-2}}$. The angular momentum of this mass thrown tangentially to the ground about Earth's center is then $R_\oplus\,m\,v$, where $R_\oplus$ is the Earth's radius. Assuming the Earth to be uniformly dense for a rough figure, its mass moment of inertia ...


11

What is the size/scale of a wood fire that is producing 1kW? Based on what my understandings re energy content of fuels and combustion processes, about 0.5 to 1 cubic inch per minute of typically dry wood in an open fire. Based on an utterly superb 80 page Wood Fuels handbook which I discovered along the way - about the same, rather to my surprise. ...


0

The polar ice will melt, due to increase of temperature in earth's surface, by global warming. The rate of cooling of earth's inner heat will be slow, resulting more molten lava in the lower mantle, will be changed into liquid. The heavier mass of the liquid will go down, resulting decrease of angular momentum. Conclusion-Increase of angular momentum of ...


23

Let's work this out from the Stephan Boltzmann law. What color is a fire? If you look at color charts for black body radiators at various temperatures, I estimate it to be about 1000K. (Be careful: some flames are colored by strong emission spectra, making their light very different from a blackbody radiator's color). Glancing around the web from various ...


2

Let's say its moving roughly 32,500 mph or about 16.316 km/s relative to the Earth. If we consider special relativity then we have ten years of seconds divided by the square root of one minus 16 kilometers per second squared over the speed of light squared. The answer turns out to be roughly half a second!


2

If you have a planet of mass $M$, then its self-gravitational binding energy is roughly $-GM^2/2R$ give or take a small numerical factor. So, for the Earth, this would be $-2\times 10^{32}$ J. Something colliding with the Earth, which has a similar mass and size, would do so at velocities of tens of km/s at least. I think the minimum closing velocity would ...


1

Anything over 500 miles in diameter, give or take is almost always sphere-shaped, the primary variation being rotation speed, which can give a flatness to the object, for example, Jupiter is visibly flattened by it's high rotational speed. The problem with building a strange shape by very large collision is that the heat generated in a collision of that ...


6

Heavier objects do not fall faster per se. But for heavy objects the influence of the air resistance will be smaller, if they have a similar surface area compared to the light objects. The answer depends on the properties of your tyres and the road. But on an even road the air resistance will typically dominate once you reach a certain speed (the friction ...


2

No and yes. At first, your assumption is not quite correct. In vacuum, all masses fall at the same speed. The reason is the that the mass cancels in the equations of motion: $ma=mg$ $a=\ddot{x}=g$ To be more precise: the inertial mass and the gravitational mass are the same. Therefore, they cancel. However, things change when you take air resistance into ...


1

I am not sure if this answer will give you an intuitive understanding of the result, but I think it may be useful as it shows the assumptions behind it. What your result means is that in an idealized situation when the volume gas or solute occupies is shrunk slightly by $\delta << V$ while its energy remains the same (let's say, isothermal compression ...


0

The short answer is, yes. The slightly longer, but slightly more accurate answer is yes, but not noticeably. As you say, increasing humidity by evaporating existing water will cause the mass of the vapor to move to a greater distance from the earth's center, and this will increase the moment of inertia, reducing the rotation rate. Consider that the ...



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