) A flat horizontal square rocket launchpad is supported by a large column at ea
ID: 1487154 • Letter: #
Question
) A flat horizontal square rocket launchpad is supported by a large column at each corner. Each side of the square faces one of the cardinal directions, North, East, South, West. Each side is 15 meters in length. The launch pad is 75,000 kg in mass. A 25,000 kg rocket sits on supports of total mass 5,000 kg centered 5 meters from the western edge of the square, exactly halfway between the north and south sides of the launchpad. What is the total force exerted by the launchpad columns on theA) Northwest and Southwest sides?
B) Northeast and Southeast sides?
Explanation / Answer
If we take the center of the pad to have coordinates (0, 0), then the center of mass of the assembly is at
.. (75(0, 0) + (25+5)(-3.75, 0))/(75+25+5) = (-15/14, 0)
The distance to the western edge is
.. (-15/14) - (-15/2) = 6 3/7 meters
The distance to the eastern edge is 15-(6 3/7) = 8 4/7 meters, which is 4/3 times the distance to the western edge.
A) The NW and SW columns together provide support for 4/7 of the 105,000 kg mass, thus 30,000 kg each. That is, each provides a support force of about 294,200 N.
B) The NE and SE columns provide support for 3/4 of the mass supported by the other columns, so 22,500 kg. The corresponding force is about 220,650 N.
_____
The support required from each of the columns will go up dramatically when the rocket is launched.
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