Class 28 Notes

# Class 28 Notes - 1 2 2 9 O r e g o n S t a t e U n i v e r...

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Unformatted text preview: 1 2 / 2 / 9 O r e g o n S t a t e U n i v e r s i t y P H 2 1 , L e c t u r e # 2 8 1 T h e f u l l y- d e v e l o p e d W o r k- E n e r g y T h e o r e m l o o k s l i k e t h i s n o w — f o u r “ s u b- a c c o u n t s ” i n t h e M e c h a n i c a l E n e r g y “ b a n k : ” E m e c h = K T + K R + U G + U S = ( 1 / 2 ) m v 2 + ( 1 / 2 ) I ¡ 2 + m g h + ( 1 / 2 ) k x 2 A n d a n y c h a n g e i n t h e t o t a l b a n k b a l a n c e m u s t b e d u e t o “ d e p o s i t s ” a n d / o r “ w i t h d r a w a l s ” — w o r k d o n e b y e x t e r n a l f o r c e s ( i . e . f o r c e s o t h e r t h a n g r a v i t y o r i d e a l s p r i n g s ) : W e x t = ¡ E m e c h O r , a r r a n g e d d i f f e r e n t l y : E m e c h . f = E m e c h . i + W e x t O r , f u l l y d e t a i l e d : ( 1 / 2 ) m v f 2 + ( 1 / 2 ) I ¡ f 2 + m g h f + ( 1 / 2 ) k x f 2 = ( 1 / 2 ) m v i 2 + ( 1 / 2 ) I ¡ i 2 + m g h i + ( 1 / 2 ) k x i 2 + W e x t 1 2 / 2 / 9 O r e g o n S t...
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Class 28 Notes - 1 2 2 9 O r e g o n S t a t e U n i v e r...

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