A horizontal aquifer is overlain by 73.5 ft of water-saturated clay with a porosity of 0.4. The solid density of the clay partic
les is 165 lb/ft3. The specific weight of water is 62.4 lb/ft3. Calculate the total stress acting on the top of the aquifer.
1 answer:
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Answer:
1) 883 kgm2
2) 532 kgm2
3) 2.99 rad/s
4) 944 J
5) 6.87 m/s2
6) 1.8 rad/s
Explanation:
1)Suppose the spinning platform disk is solid with a uniform distributed mass. Then its moments of inertia is:
If we treat the person as a point mass, then the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk:
2) Similarly, he total moment of inertia of the system about the center of the disk when the person stands at the final location 2/3 of the way toward the center of the disk (1/3 of the radius from the center):
3) Since there's no external force, we can apply the law of momentum conservation to calculate the angular velocity at R/3 from the center:
4)Kinetic energy before:
Kinetic energy after:
So the change in kinetic energy is: 2374 - 1430 = 944 J
5)
6) If the person now walks back to the rim of the disk, then his final angular speed would be back to the original, which is 1.8 rad/s due to conservation of angular momentum.