Astone is dropped at t = 0. a second stone, with 6 times the mass of the first, is dropped from the same point at t = 59 ms. (a) how far below the release point is the center of mass of the two stones at t = 430 ms? (neither stone has yet reached the ground.) (b) how fast is the center of mass of the two-stone system moving at that time?

Zirconium has an hcp crystal structure and a density of 6.51 g/cm3. (a) what is the volume of its unit cell in m3? (b) if the c/a ratio is 1.593, compute the values of c and a.

You and a friend (alex) are at a a tree-top adventure park .. . part of the course requires you to climb up a rope. you both climb the same rope in the same amount of time. however, the tension in the rope is greater when alex climbs. who did the most work? alex did - more tension means more force - more force means more work was done you did - less tension means less force - less force means more work was done to find the work done, the force exerted and distance moved are multiplied. a couch is moved twice before you are happy with its placement. the same force was used to move the couch both times. if more work is done the first time it is moved, what do you know about the distance it was moved? when more work was done, the couch was moved less. when more work was done, the couch was moved further. when more work was done, the couch wasn't moved at all. when more work was done, the couch was moved the same distance.

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.