Gold, which has a density of 19.32 g/cm3, 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 with a mass of 8.565 g, is pressed into a leaf of 4.265 μm thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.300 μm, what is the length of the fiber?

Physicians use a machine called a spirometer to measure the maximum amount of air a person can exhale (called the forced vital capacity). Suppose you can exhale 4.0L. How many kilograms of air do you exhale? Assume that the density of air is 1.3 kg/m3.

A uniform density sheet of metal is cut into the shape of an isosceles triangle, which is oriented with the base at the bottom and a corner at the top. It has a base B = 49 cm, height H = 15 cm, and area mass density σ.   a)   Consider a horizontal slice of the triangle that is a distance y from the top of the triangle and has a thickness dy. Write an equation for the area of this slice in terms of the distance y, and the base B and height H of the triangle.  b) Set up an integral to calculate the vertical center of mass of the triangle, assuming it will have the form C ∫ f(y) where C has all the constants in it and f(y) is a function of y. What is f(y)?  c)Integrate to find an equation for the location of the center of mass in the vertical direction. Use the coordinate system specified in the previous parts, with the origin at the top and positive downward.  d)Find the numeric value for the distance between the top of the triangle and the center of mass in cm.

An accomplished silversmith needs an extremely thin sheet of silver. If he starts with a 3.70-kg sheet of silver, and pounds it to a thickness of 5.00  10-7 m (a small fraction of the thickness of a sheet of paper), determine the area of the sheet he has formed. Use 10.1 ⨯ 103 kg/m3 as the density of silver.