Two identical blocks are tied together with a rope and are pulled with a second rope so that they accelerate up a rough incline. A student considering the forces
acting in this situation contends: "I think the tension in the rope connecting the
boxes has to be larger than the force the lower box exerts on that rope because
the tension is causing the lower block to accelerate up the incline."
What, if anything, is wrong with this contention? If something is wrong, identify it
and explain how to correct it. If this contention is correct, explain why

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.