Problem

Lignum vitae is a hard, durable, and extremely dense wood used to make ship bearings. A sphere of this wood with a diameter of 7.60 cm has a mass of 313 g. (a) What is the density of the lignum vitae sphere? (b) Will the sphere float or sink in water? (c) Will the sphere float or sink in chloroform? (The density of chloroform is 1.48 g/mL.)

Relevant Solution
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Hey everyone, we're told that person in wood is extremely hard, dense and wear resistant. It is used for making musical instruments, tool handles, flooring and furniture. A sphere of persimmon wood has a diameter of 8.32 centimeters and a mass of 234 g. Our first question here is asking us to calculate the density of the persimmon sphere. So as we've learned, density equals mass over volume and a volume of a sphere is going to be four thirds pi r cubed. So using this information, let's go ahead and answer A We were told that our diameter is equal to 8.32 cm. Since we need radius for our formula, all we need to do is take our diameter of 8.32 cm and divide this by two which will get us to a radius of 4. cm. Now let's go ahead and plug in our values. So we have a volume of a sphere is equal to 4/ pi R. Cubed, so 4.16 cm cubed. This will get us to a volume of 301. cubic centimeters. Now for our density, we're going to take our mass which was 234 g And divide that by our volume which is 0.5564 cubic centimeters. And this gets us to a density of 0.776 g over cubic centimeters. And since one cc is equivalent to one millimeter, We can change this to 0.776 g over millimeter. Looking at B. They're asking us to determine whether the sphere would float in water. So as we know, the density of water is equal to 1.00 g over ml. And since the density of our persimmon is less than the density of our water, this means that the sphere will float in water. Now, let's go ahead and look at C. C. Is asking us to determine whether the sphere will float in petroleum ether with a density of 0.653 g over milliliters. So first see the density of our persimmon is greater than the density of our petroleum ether. So this means the sphere will sink in petroleum either, and these are going to be our final answers. Now, I hope that made sense. And let us know if you have any questions.