Question

An iron anchor has a density of 480kg/m3 and weighs 250kg in air .if it is immersed in a sea of 64 kg/m3 how much force would be required to lift it while it is immersed?​

Answer 1

Answer:

2498

Explanation:

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Answer 2

With the density values given, the anchor would float! If you wanted to immerse the anchor, you would have to apply a downward force of 817.5 N to fully immerse this “anchor” completely under the water.

This anchor has a mass of 250 kg. Therefore, it’s weight is:

W=mg=(250kg)(9.81ms2)=2452.5N downward.

The volume of the anchor is:

V=mρ=250kg48kg/m3=5.2082m3

The buoyancy force is the weight of the water that is displaced by the volume of the anchor. Assuming that the full volume of the anchor is submerged, the buoyancy force is:

Fb=ρgV=(64kgm3)(9.81ms2)(5.2083m3)=3270N upward

Since the buoyancy force is greater than the weight of the anchor, the net force is 817.5N upward!

The actual density of iron is 7874kg/m3 and the actual density of sea water is 1028kg/m3 . Using these real numbers, the results are quite different. The weight of the anchor with a mass of 250 kg is still:

W=mg=(250kg)(9.81ms2)=2452.5N downward.

But the volume of the anchor is only:

V=mρ=250kg7874kg/m3=0.03175m3

Assuming that the full volume of the anchor is submerged, the buoyancy force is:

Fb=ρgV=(1029kgm3)(9.81ms2)(0.03175m3)=320.5N upward

Now, the net force is 2132N downward. In this more realistic scenario, the anchor is fully submerged under its own weight and a force greater than 2132N would be required to lift it.

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