"Find the net work W done by friction in pulling the board directly from region 1 to region 2. Assume that the board moves at constant velocity."

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 are two different ways you could find the value of a? explain these methods.

Aparticle moves in a circle 1.50 m in radius . through what angle in radians does it rotate if it moves through an arc length of 2.50m? what is the angle in degrees?