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.

Sorry i don’t know what to do

If the heat engine is a perfect carnot cycle engine, thenefficiency = (t2-t1)/t2   where t1=temperature of cold reservoir ( ° k) = 135            t2=temperature of hot reservoir ( ° k)   = 325thereforeefficiency = (t2-t1)/t2 = (325-135)/325 = 0.5846 = 58%  note: this is the theoretical maximum efficiency of a perfect heat engine.   real-life engines do not achieve this value.

1) what is light? light is an electromagnetic wave visible to the human eye.  2) what is a reflection? the rebounding of a light ray when it hits a mirror.3) what is the incident ray? contacts the surface of an object.4) what is the reflected ray? bounces off a reflective surface.5) what is the normal ray? perpendicular to the surface of a mirror.6) what is the angle of incidence? an angle formed by the incident ray and the normal.7) what is the angle of reflection? an angle formed by the reflected ray and the normal.8) what is refraction? (bending.)9) what is a converging lens? bring together light rays that pass through.10) what is a diverging lens? spreads out light passing through.11) focal point? the real point where the refracted rays meet when the incident rays run parallel.