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29

When you would enter the water, you need to "get the water out of the way". Say you need to get 50 liters of water out of the way. In a very short time you need to move this water by a few centimeters. That means the water needs to be accelerated in this short time first, and accelerating 50 kg of matter with your own body in this very short time will deform ...


22

It's not the falling that's fatal, it's the deceleration at the end that kills you. Something like water or concrete does this on a sub-meter distance (which requires extremely high forces). On the other hand a gas is much less dense, so it cannot decelerate a falling object nearly as quick. Sometimes inflatable cushions are used as safety nets (think: ...


12

Consider jumping into a swimming pool. Do a barrel-roll (sorry I mean cannon ball, that just kind of slipped out). It's fun, you enter the water nicely and make a huge splash, probably soaking your sister in the process (that'll learn her). Now do a belly flop. Not as fun. You displace exactly the same amount of water in the same time, but this time there is ...


11

Let's look at this another way: you're just moving from one fluid to another. Sounds harmless, right? By specification of the problem, we're at terminal velocity when we hit the water. The force of drag (in both mediums) is roughly: $$ F_D\, =\, \tfrac12\, \rho\, v^2\, C_D\, A = \rho \left( \frac{1}{2} v^2 C_D A \right) $$ You can imagine that ...


11

The ocean surface is not as hard as the ground but if you drop from a plane, you would hit it with such a high velocity that the pressure would most likely kill you or cause very serious damage. Considering air resistance, the terminal velocity of a human, right before reaching the water, would be at most some $150\text{ m/s}$. If you weigh $70\text{ kg}$, ...


6

I'm not a physicist. So I am treading very carefully attempting to answer a question here... :) A physical example that may help explain this is rock skipping. When you skip a rock, it will 'bounce' off of the water when at high speeds. Eventually it slows enough to no longer bounce but 'sink' into the water. Picture your body doing the same thing. Your ...


5

In the moist air of the clouds, the water condenses on dust particles. At the altitude where this happens, it is usually below the freezing point of water, so it quickly freezes. If winds and updrafts keep these particles of ice in the moist air, they collect more water. Eventually, the weight of the ice particles overcome the updrafts and fall to the ...


4

During a supernova, a star blasts away its outer layers; this actually reduces the mass of the star significantly. Any star or planet has an escape velocity - the slowest an object must be traveling for it to escape the gravitational field of the star/planet. For Earth, this is 11.2 km/s. (Note that this value doesn't account for any atmospheric effects.) ...


2

The formula $F=G \frac{m_1 \cdot m_2}{r^2}$ is valid only for point masses. However, it can be applied to non-point masses if its spherically symmetric. Enter Shell Theorem: 1.A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its centre. So, when a spherically symmetric ...


2

It depends what speed you are moving relative to the air (or water). If you start a jump at zero velocity relative to the air, your speed will be limited to the terminal velocity of about 125 miles/hours (at least for the density of air near ground level). An estimate of the fatal velocity relative to air is 300 miles/hour (again for the density of air ...


2

Hailstones - or anything like sleet, snow, etc - are formed by the freezing of water. Water droplets rise up, and as the temperature keeps decreasing, they freeze at a certain point into a stone, after which this stone would start falling. Certain studies say that the stone after falling, can enter an area with differenct conditions - causing it to maybe ...


1

If you were restrained, and subjected to a sufficiently powerful stream of air, it would be fatal. However, this does not happen during a jump, because you reach terminal velocity, which is typically somewhere between only 100 km/h and 200 km/h. Exposure to a wind of this velocity (which, let us say, consists of clean air that is free of debris such as ...


1

The easiest way to determine the uniformity of your slabs of wood is to take an x-ray. Seriously. This image is of an x-ray of a piece of wood where the dark regions are cavities created by termites eating away at it (the termites are the white things inside the cavities). If you don't want to take an x-ray (or can't afford one), then just assume that ...


1

The lightest gas that is stable at room temperatue is $H_2$ (two hydrogen atoms bonded to each other). At very high temperature and/or low pressure, the hydrogen molecule dissociates to become atomic hydrogen. At even higher temperature, the hydrogen ionizes. The electron is no longer bound to the proton. This is a plasma state. Electrons and protons ...


1

You are absolutely right that the limit in which this approximation holds is $$\beta(\epsilon - \mu) \gg 1 \,,$$ which is not trivially the 'high-temperature limit', and indeed looks rather like the low temperature limit. However, it also looks like the limit of large negative $\mu$. If we want to know how temperature will affect the exponent, we need to ...



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