Un corp de masă m este lansat din vârful unui plan înclinat cu unghiul  =  30 față de orizontală și lungimea = 6 m . Viteza inițială a corpului este orientată de-a lungul planului înclinat în jos și are modulul v0 = 5,0 m/s. Coeficientul de frecare la alunecare dintre corp și planul înclinat este  =  0,87 3 / 2 ( )

The key to stability is feedback between the reservoir and the fluxes into and/or out of the reservoir. assume that the rate of outflow from a reservoir depends on the size of the reservoir according to the following relationship: outflow rate= k x (size of reservoir), where k is a constant. a reservoir of water has a volume of 5000 liters, and the rate of outflow at steady state is 25 liters per minute. what is k? (give both the numerical value and its units.) what is the residence time? what is the relationship between k and the residence time?

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.

Complete these sentences. if a roller coaster train has a potential energy of 1,500 j and a kinetic energy of 500 j as it starts to travel downhill, its total energy isj. once the roller coaster train gets closer to the bottom of the hill, its kinetic energy increases to 1,100 j, and its potential energy decreases to j. when the train reaches the bottom of the track and is traveling along the ground, its kinetic energy isj.