1) In 20 seconds of freefall, an object will travel approximately 1.96 kilometers. What is this value expressed in centimeters, and written in scientific notation? 2) Convert 365 micrograms to grams. 3) A mineral called iron pyrite forms crystals that are shaped like rectangular boxes. One such crystal is 8.6 ∗ 10^(− 3) meters tall, 5.0 ∗ 10^(− 2) meters wide, and 7.8 ∗ 10^ (− 2) meters deep. Ignoring significant figures, what is the volume of this rectangular crystal? Please answer once you can, thank you.

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.