下午5:51 3月21日周一 45%O T + : U and to convert from polar coordinates to Cartesian: (9) x= r cos o y=rsino Î = cospf – sino;

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下午5:51 3月21日周一 45%O T + : U and to convert from polar coordinates to Cartesian: (9) x= r cos o y=rsino Î = cospf – sino; Û= sin of + cos 06. (10) 3. [8 pts.] Force and potential Consider the force potential U = (x² + y2)-2, which is related to the force by, F =VU. + (a) What is the force? (b) While we will often assume the Earth is flat to simplify the physics, we live on a sphere, not a flat world (nevermind the Flat Earth Society). In some cases, the formulation is made with respect to spherical coordinates (latitude, longitude, depth is one such system), and in others we want to convert from Cartesian to spherical coordinates. Х Convert the above result into polar coordinates. (c) Graph the force field as a function of radius. (d) What is the shape of the equipotential surface? (Think two dimensions, not just the one shown on your graph.) < P > #