problem07_78

University Physics with Modern Physics with Mastering Physics (11th Edition)

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7.78: a) x m ma F x dt x d a x x x 2 0 2 0 2 2 , ϖ ϖ - = = - = = y m ma F y y dt y d a y y y 2 0 2 0 2 0 2 2 , ϖ ϖ ϖ - = = - = - = = b) [ ] [ ] ) ( 2 1 2 2 2 0 2 0 y x m ydy xdx m dy F dx F U y x + = + = + - = ϖ ϖ c) ) ( cos ) ( sin 0 0 0 0 0 0 0 0 0 0 0 0 x x y t y dt dy v y y x t x dt dx v y x ϖ ϖ ϖ ϖ ϖ ϖ + = + = = - = - = = (i) When 0 x x = and 0 , 0 = = x v y and 0 0 ϖ y v y = ) ( 2 1 and 2 1 , 2 1 ) ( 2 1 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 2 y x m U K E mx U my v v m K y x + = + = = = + = ϖ ϖ ϖ (ii) When 0 = x and 0 0 0 , ϖ x v y y x - = = and 0 = y v ) ( 2 1 and 2 1 , 2 1 2 0 2 0 2 0 2 0 2 0 2 0 2 0 y x m U K E y m U mx K + = + = = = ϖ ϖ ϖ
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