You are designing a 108 cm3 right circular cylindrical can whose manufacture will take waste into account. there is no waste in cutting the aluminum for the side, but the top and bottom of radius r will be cut from squares that measure 4r units on a side. the total amount of aluminum used up by the can will therefore be upper a equals 32 r squared plus 2 pi rh, where h is the height of the right circular cylindrical can. what is the ratio of h to r for the most economical can?

The speed of light in a material is 0.50 c. what is the critical angle of a light ray at the interface between the material and a vacuum?

Antireflective coatings on solar cells are often made by applying a thin film of silicon nitride (sinx), which has an index of refractive of 1.2, on the top of the silicon solar cell, which has a refractive index of about 3.5. however, the sun emits radiation of various wavelengths which the solar cell absorbs, and the antireflective coating can only absolutely minimize the reflection of one of these wavelengths. the coating thickness is chosen to reduce the reflection of green/yellow light (e = 2.2 ev), which is the most intense color in the solar spectrum (shown below). which of the following coatings would minimize reflection of green/yellow light? the answer is 820 nm how? what is the angular width of the central maximum of an electron traveling at 2 x 108 m/s going through a single slit of width 1 mm.

Aprotein molecule in an electrophoresis gel has a negative charge. the exact charge depends on the ph of the solution, but 30 excess electrons is typical. what is the magnitude of the electric force on a protein with this charge in a 1600n/c electric field? write in two significant numbers, and also in newton