Scientists are trying to determine the effect of mass on the force of gravity between two objects. in this experiment, then scientists use the following procedure: 1) place two large, empty barrels exactly 1m apart. 2) measure the gravitational force between the two barrels and record in data table. 3) add 10kg of water to each barrel. 4) measure the gravitational force between the two barrels and record in data table. 5) repeat steps 3 & 4 until the barrels are completely full of water. 6) create a graph of gravitational force vs mass from the data collected. what should the graph from step 6 look like?

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.