A semi-truck with mass mt = 15,000 kg, traveling in the direction of traffic at vt = 35 m/s, undergoes a perfectly inelastic collision with a passenger car of mass mc = 1,250 kg, traveling in the same direction at vc = 20 m/s. Which statement describes the final kinetic energy of the semi truck?

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.