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Half. The escape velocity for an object at a distance $D$ from an object of mass $M$ is $\sqrt{2GM/D}$. The circular orbital velocity (the Moon is on an orbit that's close enough to circular that I'll just assume this) at the same distance is $\sqrt{GM/D}$. Setting the escape velocity from the Earth with it's new reduced mass $M_{\rm new}$ equal to the ...

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Assuming that we are making a certain amount of the earth's mass disappear instantly somehow, doing this will decrease the escape velocity of the earth. The moon is already moving at its orbital velocity in an orbit centered on the current center of mass of the earth-moon system. If we took away so much mass (instantaneously, somehow) that the escape ...

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When you jump from a height, you gather momentum. Absorbing this momentum at landing reduces the size of the maximum force, and thus the "pain". Let us assume that the distance over which a person can absorb the momentum of the fall is proportional to their height (proportional to the length of their legs). In that case, the taller person can absorb the ...

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This kind of question is more easily, quickly and reliably answered by doing an experiment, rather than a calculation. The calculation requires you to decide what are the most important mechanisms for heat loss, what formulas to use, how to take account of the shape of the container, then measure all dimensions, find the appropriate data (thermal ...

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First get data lined up. It seems the container is not small :) volume of water: $4.80\times 10^{-4}~m^3$ heat transfer surface area (ignore wood supporting face): $0.038m^2$ mass of water: $0.48~kg$ heat capacity of water is 4.2kJ/kg-K calculate how much heat required for the water to reach room temperature. $$\bigtriangleup Q=m c (27-10)= 34.3kJ$$ ...

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As a rough estimate: we can approximate the shape of the can with a cylinder of radius $R=3,2$ cm and height $h=15,5$ cm (those are the dimensions of a Cola can). Its total area can be found by using $$A_T=A_L+2A_B= 2\pi R h + 2\pi R^2$$ which gives us $A_T$=$375,8$ cm$^2$. Assuming that water vapor condensation forms a 1 mm thick, continuous sheet of ...

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The force straining a grain (which may soon be squashed) is equal and opposite to the weight (gravity force) supplied by the grain pile above. That's Newton's third law. If ALL the weight of the pile were held up by one single kernel, F_grain ~= Mass_of_pile * g and it would be easy for the ton of grain to smash the bottom kernel. It doesn't work ...

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The physical processes that control the structure of conical piles are fascinating and imperfectly understood even today. However we can approach your question in approximate way. The angle that the surface of the pile makes with the ground is called the angle of repose. Predicting this theoretically is hard because it is is sensitive to the exact nature of ...

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First off I would recommend a very large boot. "Size billion" comes to mind. Second I would query "in what direction are you planning to kick said ball with said billion sized boot, fine sir?" Since direction is not specified in this...ahem...matter...ahem...I find the issue at hand confounding indeed. Still...we all could use a few more hours in our day ...

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This is similar to Can humans control rotation of the Earth? and How can you find the impact necessary to change the direction of Earth's spin? Suppose the ball is kicked against the direction in which the Earth is rotating. This increases the speed of rotation of the Earth, reducing the rotation period (ie the length of 1 day). The angular momentum ...

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Pressure drop in duct flow For fluid flow through a duct, we normally talk about pressure drop, not drag. Pressure drop is usually expressed as $\Delta p=\xi\rho V^2/2$, where $\xi$ is the minor loss coefficient (minor as opposed to major, which refers to pressure drop over a long straight pipe). In a case like this, you will have an additional loss due ...

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Indeed, a nuclear bomb works a bit differently in a vacuum than in the atmosphere. If you want to generate momentum, an atmosphere or some material with a low boiling point (e.g. ice) is probably better than bare rocks in vacuum, because all the heat will be converted directly into gas with a high momentum, without "wasting" energy on heating and evaporating ...

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