1. The problem statement, all variables and given/known data Gold, which has a density of 19.32 g/cm^3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold, witha mass of 27.63g, is pressed into a leaf 1.000 µm thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.500 µm, what is the length of the fiber? 2. Relevant equations ρ=m/V (density) 3. The attempt at a solution Im having trouble finding a direction to go in. I think converting to density is the way to go but I am having trouble using the density formula as well.
But aren't you given the density: 19.32? Hint: You need to know volume of a cylinder, and that other thing (cube ?) in order to solve this. So, I guess both require two steps.
Ok so my intial direction was right but the problem I am having now the area. It just doesnt make sense how I can take the density and find the area. The set-up is not making sense.
first find the relationship between area and volume and then between volume and density/mass and you will get the area
I got it. Thanks for the help the relationship is what I was confusing but all I had to do was divde the density by the mass to get rid of the grams and then convert the cm^3 to µm^3 and relate the area and volume as you said and then the volume with the area. Thanks
You need to find a relationship between area and volume for the shape you are considering. For gold leaf, assume that you are using the equation for 2 faces of a cube of material and for a rod assume the area is limited to that of a rod minus the ends.
But what kind of formula should i use for 2 face cube and also for the rod Thanks for replaying back.
Using the example of the gold leaf, assume you have a collection of finite elements, each of which is a cube of the same dimension as the thickness (w= 1.000 µm) of the foil. The area of each face of the cube will be w^{2} and you need two of 'em. Next, you need to understand that the total volume of the gold will be N*w^{3} where 'N' is equal to the number of elements of dimension w X w X w. Can you get there from here?