How does changing the threads on a screw affect the force and distance required to perform work?

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.

Which best describes how fluids change as they travel through different portions of the convection currents? they change to solids at the outer portion of the convection currents. they change to solids at the inner portion of the convection currents. they become more dense at the outer portion of the convection currents. they become more dense at the inner portion of the convection currents

In a hydrogen molecule there are a total of four charges, 2 protons in the two nuclei, and 2 electrons. how many unique charge-pairs are there (without double counting)?