a bucket of water with total mass 23kg is attached to a rope, which in turn is wound around a 0.050 m radius cylinder, with crank, at the top of a well. the moment of inertia of the cylinder and crank is 0.12 kgm².the bucket is raised to the top of the well and released to fall back into the well. what is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 8.0 m/s?​

Aparticle of mass m is placed in a one-dimensional box of length l. the box is so small that the particle’s motion is relativistic, so that e p2/2m is not valid. (a) derive an expression for the energy levels of the particle using the relativistic energy–momentum relation and the quantization of momentum that derives from connement. (b) if the particle is an electron in a box of length l 1.00 1012 m, nd its lowest possible kinetic energy. by what percent is the nonrelativistic formula for the energy in error?