Friction: a) comes from microscopic bumps that act as obstructions to the object's motion. b) is the name given to the force acting between surfaces sliding past one another. c) acts in a direction that opposes the motion of an object. d) none of the above e) a, b and c

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.

Matter is needed to transfer thermal energy bya. conductionb. convectionc. radiation d. both a & b.

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