What is the minimum kinetic energy needed to launch a payload of mass m to an altitude that is one earth radius, re, above the surface of the earth (the payload will then fall back to earth)? (note that me is the mass of the earth.)

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.

In order to do work, the force vector must be question 1 options: in a different direction than the acceleration vector. in a different direction than the displacement vector. in the same direction as the displacement vector and the motion. in the same direction as the acceleration vector.

The electric potential a distance r from a small charge is proportional to what power of the distance from the charge? a. r^-1 b. r c. r^-2 d. r^2