You purchase a rectangular piece of metal that has dimensions 5.0 mm ×15.0 mm ×30.0 mm and mass

You purchase a rectangular piece of metal that has...

You purchase a rectangular piece of metal that has dimensions 5.0 $\mathrm{mm} \times 15.0 \mathrm{mm} \times 30.0 \mathrm{mm}$ and mass 0.0158 $\mathrm{kg}$ . The seller tells you that the metal is gold. To check this, you compute the average density of the piece. What value do you get? Were you cheated?

You purchase a rectangular piece of metal that has dimensions 5.0 $\mathrm{mm} \times 15.0 \mathrm{mm} \times 30.0 \mathrm{mm}$ and mass 0.0158 $\mathrm{kg}$ .
The seller tells you that the metal is gold. To check this, you compute the average density of the piece. What value do you get? Were you cheated?

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Key Concepts

Material Properties Comparison

Comparing the computed density with the expected density of a material, such as gold, allows one to assess whether a material is as claimed. A significant discrepancy between the calculated density and the known standard indicates a potential issue, such as misidentification or fraud.

Unit Conversion

Unit conversion is crucial in any physical calculation to maintain consistency. For example, when dimensions are given in millimeters but standard densities are in grams per cubic centimeter, converting the units properly is necessary for an accurate density calculation.

Volume Calculation

Calculating the volume of an object involves using its dimensions. For a rectangular prism, the volume is found by multiplying its length, width, and height. Knowing the volume is essential for determining density when the mass is known.

Density

Density is a fundamental physical property defined as the mass of an object divided by its volume. It is used to characterize materials and can be used to verify a substance's identity by comparing the computed density with known standard values.

Transcript

00:01 This problem tells us we're given a material with dimensions 5mm by 15 millimeters by 30 millimeters, and we're told it has a mass of 0 .058 kilograms.

00:12 And our question is, as we are wondering, is if this material is made of gold.

00:17 In order to do that, what we can do is we can compare the density of our given material to the density of gold.

00:24 And that's something that we can look up in our text.

00:26 So i'm going to write row of gold is equal to, it's 19 .3 times 10 to the 3 and that is in kilograms per cubic meter.

00:42 What i'm going to need to do is i'm going to need to find the density of my given material.

00:47 In order to do that, i know that density is equal to mass divided by volume.

00:54 I'm going to look at where i can find those values.

00:56 To find mass, i can see that i'm given it nice and easy.

00:59 To find a volume, i'm going to need to use these dimensions that i was given.

01:05 I should know that volume is equal to length, times width, times height.

01:09 So to find that, i am going to do my 5 millimeters times 15 millimeters times 30 millimeters.

01:21 And then i find that my volume is equal to 20 to 50.

01:27 And that's in cubic millimeters.

01:30 Now, the density i was given for gold is in cubic meters...

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