Rosa eats a peanut butter sandwich for lunch. Peanut butter contains a lot of protein, and bread is mostly starch. Rosa plans to go for a run later this
afternoon. Rosa is breathing normally.

If you wanted to move an electron from the positive to the negative terminal of the battery, how much work w would you need to do on the electron? enter your answer numerically in joules.

Explain what will happen if decomposers were apsent from a forest ecoysystem.

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.