For a specific polymer, given at least two density values and their corresponding percent crystallinity values, develop a spreadsheet that allows the user to determine the following: (a) the density of the totally crystalline polymer (b) the density of the totally amorphous polymer (c) the percent crystallinity of a specified density (d) the density for a specified percent crystallinity

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

At very high pressures, gases become and will eventually a) more dense; become hotter b) more dense; change to a liquid or solid c) less dense; combust d) less dense; turn into a liquid

Suppose a wire with a current is pushed upward by a magnetic field. how would the wire move if the direction of the current reversed? explain your answer.