When a parachute opens, the air exerts a large drag force on it. This upward force is initially greater than the weight of the sky diver and thus, slows him down. Suppose the weight of the sky diver is 913 N and the drag force has a magnitude of 1010 N. The mass of
the sky diver is 93.2 kg. Take upward to be the positive direction. What is his acceleration, including sign?

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.