A 10kg block of aluminum (p=2700 kg/ m^3) is attached to a rope. Find the tension force in the rope if the block is in vacuum? What is the tension force in the rope if the block is in air (p=1.29 kg/m^3) and What is the tension force if the block is in water?
I. Find the tension force in the rope if the block is in vacuum?
In vacuum medium FB = 0 because vacuum density = 0.
Rope tension T = F = mg = 10 kg * 9.81 m/s2 = 98.1 N.
II. What is the tension force in the rope if the block is in air (p = 1.29 kg/m3)?
V = 10kg / 2700kg/m3 = 0.0037 m3
FB = 1.29kg/m3 * 9.81m/s2 * 0.0037 m3 = 0.047 N.
T = F - FB = 98.1 - 0.047 = 98.053 N.
III. What is the tension force if the block is in water?
Water density is 1 g/L = 1000 kg/m3.
FB = 1000 kg/m3 * 9.81m/s2 * 0.0037 m3 = 36.3 N.
T = F - FB = 98.1 - 36.3 = 61.8 N.
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