What is the velocity of a 500-kilogram elevator that has 4,000 joules of energy?

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.

A100-watt light bulb illuminates a solar cell. the electricity from the solar cell operates a water pump that delivers 1 watt of power. what is the efficiency of the system?

Place several e-field sensors at a few points on different equipotential lines, and look at the relationship between the electric field and the equipotential lines. which statement is true? 1-at any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of higher voltages. 2-at any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of lower voltages. 3-at any point, the electric field is parallel to the equipotential line at that point.