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69Mustang
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While mowing the grass, I thought of the following problem (to take my mind off of the heat!)
Consider a vertical column of water in a container. The pressure exerted by the water on the sides of the container is rho x g x h, where rho is the density of the water, h is the height of the column above the specific vertical location being considered. Remember that the pressure doesn't depend on the horizontal size. Now, if the strength of the container material (measured in pressure units) is too small (less than the pressure at that point), the container breaks. An observer sitting at rest w.r.t. the column observes the container is not breaking.
Another observer is moving rapidly, perpendicular to the column (horizontally). The width of the container is contracted and the mass is increased according to most explanations. Also, the walls become thinner. Therefore, the density of the the liquid increases by approx. (gamma)^2. Yet, the container cannot break because the other observer doesn't see it.
Is the strength of the material greater in the improper frame? If so, why? One might say the intermolecular distances contract, but only in the horizontal direction, and the strength that's important is the shear strength between different heights; that spacing hasn't changed, has it? Why doesn't the thinning of the walls make the wall weaker?
Or maybe the density doesn't change? If not, why not? You still have the problem of thin walls.
Explanations, please? Hope this tickles a bit.
BN
Consider a vertical column of water in a container. The pressure exerted by the water on the sides of the container is rho x g x h, where rho is the density of the water, h is the height of the column above the specific vertical location being considered. Remember that the pressure doesn't depend on the horizontal size. Now, if the strength of the container material (measured in pressure units) is too small (less than the pressure at that point), the container breaks. An observer sitting at rest w.r.t. the column observes the container is not breaking.
Another observer is moving rapidly, perpendicular to the column (horizontally). The width of the container is contracted and the mass is increased according to most explanations. Also, the walls become thinner. Therefore, the density of the the liquid increases by approx. (gamma)^2. Yet, the container cannot break because the other observer doesn't see it.
Is the strength of the material greater in the improper frame? If so, why? One might say the intermolecular distances contract, but only in the horizontal direction, and the strength that's important is the shear strength between different heights; that spacing hasn't changed, has it? Why doesn't the thinning of the walls make the wall weaker?
Or maybe the density doesn't change? If not, why not? You still have the problem of thin walls.
Explanations, please? Hope this tickles a bit.
BN