Sapphire has an index of refraction of 1.77. The critical angle for sapphire in air with an index of refraction of 1.0 is degrees.

Ball b is hanging from an inextensible cord. an identical ball a is released from rest when it is just touching the cord and drops through the vertical distance h a 5 8 in. before striking ball b. assuming e 5 0.9 and no friction, determine the resulting maximum vertical displacement h b of the ball b

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.

What occurs during a combustion reaction