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Unformatted text preview: Physics 341: Problem Set #1 Solutions 1. (a) Use dimensional analysis to derive a relationship between the total mass of a gravitationally bound system M , its typical size R , and the typical speed v of its components. We can start by writing the dimensions for the quantities involved, as well as Newtons gravitational constant (because gravity is holding the system together). gravity G [ M- 1 L 3 T- 2 ] mass M [ M ] size R [ L ] speed v [ LT- 1 ] If we solve for the speed, some trial and error quickly yields v GM R 1 / 2 Or similarly, we could have solved for the mass or the size M v 2 R G R GM v 2 (b) A globular cluster has about 10 6 stars in a sphere of radius 10 pc. Using your analysis above, estimate the speed with which the stars move inside the cluster, in units of km s- 1 . You will need to make an assumption about the average star; be sure to state any assumptions explicitly. We need to know the mass of the cluster, so well have to make an assumption....
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This note was uploaded on 10/18/2011 for the course PHYSICS 341 taught by Professor Keeton during the Fall '08 term at Rutgers.
- Fall '08