Two masses m 1 and m 2 move i n a plane and interact by a potential energy U (r) = f kr 2 • Write down their Lagrangian in terms of the CM and relative positions R and r , and find the equations of motion for the coordinates X, Y and x, y. Describe the motion and find the frequency of the relative motion.

Chemical energy sources are often portable and provide large amounts of energy. fossil fuels are one kind of chemical energy source. most of the energy we use in the united states is generated by the combustion of fossil fuels. however, fossil fuel combustion adds greenhouse gases to the atmosphere, mostly co2. one measure of the total amount of greenhouse gases that are emitted into the atmosphere each year is called a carbon footprint. read this article to compare the carbon footprint of an average person in the united states to an average person around the world. knowing that greenhouse gases are contributing to climate change, how can we reduce our carbon footprint, particularly in the united states? could hydrogen fuel replace fossil fuels in the future? why or why not? should the size of a person’s carbon footprint be limited by law? why or why not?