A crane is used to lower weights into the sea(density = 1025 kg/m^3) for an underwater construction project. Determine the tension in the rope of the crane due to a rectangular 0.4m x 0.4m x 3m concrete block (density = 2300 kg/m^3) when it is completely in the air and completely immersed in water. Answers in kN

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The block has a volume of 0.4 * 0.4 * 3 = 0.48 m3

So it has a mass of 2300 * .48 = 1104 kg

Therefore the tension in the rope when it is out of the water is mg

= 1104 * 9.81 = 10830 N = 10.83 kN

In the water, it displaces 0.48 m3 of water which has a mass of 0.48 * 1025 = 492 kg

So the tension in the rope when it is in the water is (mblock-mwater)g

= (1104 – 492) * 9.81 = 6004 N = 6.00 kN

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