Problem Set 5

# Problem Set 5 - Problem Set V- Assign October 2, 2006 Due...

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Problem Set V- Assign October 2, 2006 Due October 9. Fall 2006 Physics 200a R. Shankar Many problems ask for answers in terms of symbols and not numbers. You may need to invoke things like g in the answer even if I did not explicitly de±ne them. 1. Consider masses m 1 ,m 2 ,m 3 at x 1 ,x 2 ,x 3 . Find X , the CM coordinate by ±nding X 12 , the CM of mass of 1 and 2, and combining it with m 3 . Show this is gives the same result as X = 3 i =1 m i x i 3 i =1 m i 2. Consider a square of mass 4 kg, side 2m, negligible thickness, with its sides oriented along the usual axes with its center at (0 , 0). (i) Determine its CM using symmetry arguments. (ii) Imagine that the 1m × 1m part of it in the fourth quadrant is chopped oﬀ. Where is the new CM? Do this using the extension of result in previous problem. Repeat using the following trick: view the chopped oﬀ shape as the full square plus a 1m × 1m square of negative mass - 1kg in the fourth quadrant. (iii) A disk of radius R centered at the origin has a circular hole of radius

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## This note was uploaded on 07/13/2008 for the course PHYS 200 taught by Professor Ramamurtishankar during the Fall '08 term at Yale.

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Problem Set 5 - Problem Set V- Assign October 2, 2006 Due...

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