Write downthe Lagrangian L(xj, x 2 , i 1 , i 2 ) fortwoparticlesof equal masses. rnj = m2 = m, confined to the x axis and connected by a spring with potential energy U = !kx 2 • [Here x is the extension of the spring, x = (x 1 - x 2 - l), where l is the spring's unstretched length, and I assume that mass 1 remains to the right of mass 2 at all times.] Rewrite .C in terms of the new variables X = !(x 1 + x 2 ) (the CM position) and x (the extension), and write down the two Lagrange equations for X and x. (c) Solve for X (t) and x(t) and describe the motion.

According to the phase diagram for water, how is the state of water determined? proceed up a vertical line at any given temperature read the phase at the intersection of any given temperature and pressure at a given pressure, proceed horizontally to the s-l or l-g line

What is the length x of the side of the triangle below? (hint: use the cosine function)

Beryl states that insulation with the smallest possible thermal conductivity is best to keep a house warm in winter, but worst for keeping a house cool in summer. sapphire insists the reverse is true: low thermal conductivity is good in the summer, but bad in the winter. which one, if either is correct? a. beryl, because low thermal conductivity results in low heat transfer. b. beryl, because low thermal conductivity results in high heat transfer. d. sapphire, because low thermal conductivity results in high heat transfer. e. neither, because low heat transfer is desirable both in summer and in winter.