Weight, what?

Classical Mechanics Level 2

An object weighs 22 N 22N in water and 30 N 30N in oil, whose specific gravity is 0.82 0.82 . In two decimal places, what is its weight in air, in Newtons? For the problem, use the standard unit weight of water as 9810 N / m 3 9810 N/m^3 .


The answer is 66.44.

Juvin Abayon by Juvin Abayon , 24, Philippines

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1 solution

Juvin Abayon
Oct 26, 2017

Suppose that the object has a volume V V cubic meters and weighing W W Newtons. Being fully submerged in the liquids specified, the displaced volumes would then be equal to V V as well, having buoyant forces 9810 V 9810V and 9810 ( 0.82 ) V = 8044.20 V 9810(0.82)V = 8044.20V Newtons.

The respective buoyant forces and the submerged weights are all directed upward; whereas the weight of the body itself, downward. Hence, by vertical force summations in each of the cases,

Water : 9810 V + 22 = W 9810V + 22 = W

Oil: 8044.20 V + 30 = W 8044.20V + 30 = W

Solving the set of equations give V = 0.0045305 V = 0.0045305 m 3 m^3 and consequently, W = 66.44 N

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