Does Iron Float in Mercury? Relative Densities

19Mar 2014 by Vincent Summers 1 Comment

Both substances are heavy and mercury is a liquid, so what do you say? Does iron float in mercury?

Mercury is a liquid; some objects should float in it. There are two factors that must be taken into consideration in order to answer the question, Does Iron Float in Mercury? Those two factors are the density of the material under consideration and its geometry. Our focus for this discussion will center on a block of solid iron, 4 cm x 4 cm x 4 cm.

Density – the Numbers

A material floats if it possesses a lower density. Iron’s density is 7.9 g/cm³ (grams per cubic centimeter). Mercury’s density is 13.5 g/cm³. The iron presses on the mercury, but because it is lighter, it floats. There will be some submersion, however, even as a boat floats on water, but part of it rests within the water. The submersion depth may be calculated, but requires that one puts on his thinking cap.

Degree of Submersion

The area of the base — the surface area of the iron contacting the mercury — we will call S, which equals 4 cm x 4 cm = 16 cm². All the weight of block centers on the 16 square centimeters. The iron’s weight totals 7.9 g/cm³ x 64 cm³ or 505 g. As far as the mercury is concerned, the density of the iron appears to be 505 grams divided by S x D, or the surface area times the depth of penetration. This apparent density decreases the more the iron penetrates the mercury. It penetrates until it equals the actual density of the mercury, 13.5 g/cm³.

So,

505 / (16 x D) = 13.5

which, by rearrangement, may also be written

D = 505 / (16 x 13.5)

D = 2.34 centimeters.

So Does Iron Float in Mercury?

The iron floats and does not sink. If it sank, all the iron would lie below the surface of the mercury. However, the depth the iron penetrates the mercury is considerable, and amounts to 2.34 centimeters. 1.66 centimeters of the iron block lies above the surface of the mercury. If the were pounded out into metal sheet and made into a kind of boat, much more of it would lie above the surface.

Here is a photo of an iron “nut” floating in a dish of mercury.

Note: You might also enjoy Crookes Radiometer – How Does It Work?

References:

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