# Answer to Question #105358 in Mechanics | Relativity for Jake

Question #105358
1. A block of stone of mass 30 kg (S.G. 3) hangs from a cord and is completely immersed in water. Find the tension in the cord.
1
2020-03-16T12:23:24-0400 Here T is the tension in the cord, mg is the gravity force, Fa is the Archimedes' force. Also given that m = 30 kg and "S.G. = \\dfrac{\\rho_{stone}}{\\rho_{water}}", g = 9.8 m/s^2

Solution

As far as the stone does not move, the sum of up and down forces isp equal to zero. Thus:

"T + F_a = mg \\Rightarrow T = mg - F_a.\\\\"

By definition, "F_a = \\rho_{water}gV," where "V" is the volume of stone: "V = \\dfrac{m}{\\rho_{stone}}."

Putting all together, "T = mg - \\rho_{water}g\\dfrac{m}{\\rho_{stone}} = mg(1-\\dfrac{1}{S.G.})\\\\" .

"T = 30\\cdot 9.8 \\cdot \\dfrac{2}{3} = 196"

Answer. The tension in the cord is 196 Newtons.

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