PHYS 2212 Problem-Solving Studio #3 YOUR Name Your Team Members Gauss's Law Adapatation You are watching an episode of Doctor Who, in which the thirteenth Doctor is falling down a mineshaft drilled from the surface of a planet all the way to it's center. As she falls, she scans with her sonic scredriver, and reassures her Companions that, since the density of the planet decreases linearly to zero at the center, they are in no danger because their acceleration will also decrease linearly toward zero at the center. Watching the show, you are concerned that perhaps the writers of the programme did not get the physics right. Recalling that the Law of Gravitation is mathematically identical to Coulomb's Law- and having just studied Gauss's Law in your Electromagnetism class you realize that a gravitational analog of Gauss's Law (see below) will help you answer the question. Instructions: A. Formulate a specific physics problem that will answer the question posed. Include a visual representation of the situation described, with all physical quantities represented by symbolic variables. Identify the concepts that will be needed to answer the question posed, as well as any simplifying assumptions that you will use. Outline a plan (i.e. a series of specific analytical steps) that you will use solve the problem. B. Solve the problem that you formulated in Part A, using the physics approach you have identified. You may consult with your team members, but each of you should individually write up your own solution. Gravitation Electrostatics Qq Force: Fg = G Mm r2 -(-) Force: 7 = 47tgrz (+) Field: = ,- (-1) Field: = = a Q 4r2 (+) +Qin Gauss's Law: $g. 8A = -41G Min Gauss's Law: $ S = EO (Make sure you understand why there is a minus sign in the gravitational form of Gauss's Law!)