Tutor profile: Harsh B.
Subject: Mechanical Engineering
How many independent elastic constants exist for an anisotropic linear elastic material?
The fourth-order stiffness tensor contains at most 81 elastic constants, but since it has both major and minor symmetries, this number reduced to 21 for a general anisotropic linear elastic material. If the material is isotropic, the number of constants further reduces to only 2.
Find the limit of ln(3t)/t^2 as t approaches infinity.
First, we observe that as t approaches infinity, both the numerator and denominator approach infinity. This means we can use L'Hospital's rule. Taking derivatives of both the numerator and denominator: (1/t)/(2*t) = 1/(2*t^2) Now as t approaches infinity, we see the expression goes to zero.
You are in a canoe in a pool. You mark the water level at your side. You have a rock in the canoe. You throw it overboard and it sinks to the bottom. What happens to the water level?
The key concept here is buoyancy, which is proportional to the volume of fluid displaced. When the rock is inside the canoe, the volume of the water displaced is [(M+m)/w] where m = weight of rock, M = weight of canoe, and w = density of water. When the rock is thrown overboard, the volume of the water displaced is [M/w + m/r] where r = density of rock. Subtracting these two equations, we find that the volume change of the displaced water is [m/w - m/r]. Since the rock sinks, its density is greater than that of water, i.e. r > w. This means the volume change is positive and more water is displaced when the rock is in the boat. Therefore, when the rock is thrown overboard, the water level falls.
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