HW 2-1

1 2 4 × y Z > u , T 2 E H ◦ = r ✗ E F i n = r × m i r , = r t r i ' H o = I I ( r x m . i t = £ / 2 m 2 m m = 2 0 k g , n s t a r t s : p - 0 V 0 k c o n s e r v a t i o n o f e n e r g y : K E , + P E I = K E T , + V 1 = T V i + m g h , + ± K X ? = ± m 2 + P E Z 2 + V 2 ⟂ m Z V 2 2 + m g h z + ± 4 × 2 2 e n d s : s t o p s w h e n 4 = 0 . 5 m u n s t u c k e d l e n g t h = 1 m V 2 = 0 I K ( x - X o ) ? = m g h z + ± K I X - ✗ 0 1 ? I H I X - x . f i - ± K ( × - X o ) } = - m g h z K # ( x - x o l i - 1 1 × - 0 1 } / = - m g h z 2 . 4 / 1 1 2 - 1 1 2 - 2 1 1 2 - + 0 . 5 2 - 1 ) ² ) = - 2 0 / 9 . 8 1 ) ( 0 . 5 ) K = 9 8 . 1 c ² = 9 2 + 6 2 C = 2 2 + 0 . 5 2 0 . 5 2 c F i n a l : - K = 7 7 3 . 1 1 M m 0 . 1 2 6 8 9 3 7 i n + 1 0 i n + B c 2 0 " • c o n s t a n t v e l o c i t y V A = 5 0 0 m m / s a ) t h e a n g u l a r v e l o c i t y o r t h e r o d b ) t h e v e l o c i t y o f e n d B o f t h e r o d d e t e r m i n e : a ) W = I O 7 t a n o = ½ = 0 . 7 → 0 - 3 5 ° A C = 1 0 c o s o 1 0 = 1 2 . 2 1 i n C B = 2 0 - 1 2 - 2 1 = 7 . 7 9 i n V A = 1 9 . 6 9 1 h / s 1 0 9 0 V A = 2 5 1 h / s V c V c / a W = V c / A = 1 9 - 6 9 5 m 3 5 ? A C 1 2 . 2 1 " 1 0 V B V c / B V c > β 0 . 9 2 5 r a d I s A n g u l a r a c c e l e r a t i o n o f o s c i l l a t i n g d i s k α : - ¥ 0 a ) F i n d K , w - 8 r a d / s 0 = 0 , a n d 0 - 4 r a d W = 0 α - W f p → W h y = - 4 0 W d w = - K O d o ◦ w d w = 1 " - K o d o y ° = - K ♀ , 1 1 0 2 8 2 ) = - # ( 4 2 - 0 2 ) £ 1 6 4 1 = - ¥ 1 1 6 ) 3 2 = 8 K → K = 4 5 - 2 8 Y 2 b ) F i n d W w h e n D = 3 r a d W d w Ñ d w = - 3 K O d o - = - K O d o ± W ² " = - ½ 4 0 2 8 O 3 ½ ( w ' - 8 4 = - 2 4 / 3 2 - 0 2 ) ± ( w ² - 6 4 1 = - ½ 4 1 9 - 0 1 W ² - 6 4 = - ( 4 × 9 ) w ² = - 3 6 + 6 4 = 2 8 W = 5 . 2 9 r a d I s 5 α A B = 6 r a d 1 5 W A B = 3 r a d / s F i n d : α e D B 0 . 5 m I B A c 0 . 5 m - I m D • A I m ✗ A B W A B V B W B C A B V c L I N K A B - L A B I W A B V B A B A B W - ¥ W A B = ¥ ⅔ V B = W A B . R A B V B = 3 × 1 = 3 m 1 5 A B = α A B ✗ T A B - W A B ² T A B = - 6 K ✗ ( i i ) - ( 3 ) ( i i ) = f - 9 1 - 6 5 1 m s L I N K C D V c = W C D . R C D V C = W C D • ( 0 . 5 m ) A c = α C D ✗ R C D - W C D ² R C D A c = α C D K ✗ 1 - 0 . 5 9 ) - W e d - ( - 0 . 5 9 ) = 0 . 5 α C D ↑ + 0 . 5 W c p ? J , ↗ 8 5 m n T 1 m A B V B c W B C V c T B = 0 . 5 m r e = 1 m V B - R B W B C V c = r e W B C → V c = ( 1 ) ( 6 ) W e d = ¥ , = ¥ , = 1 2 r a d / s I I c → W B C = Y B , = £ , = 6 r a d / s = 6 m / s A c = A B + α B C X T C / B - W B C ² . F C B 0 . 5 α C D ↑ + 0 . 5 ( 1 2 ) ² j = ( - 9 9 - 6 5 ) + ( - ✗ B C i ) ✗ ( - 0 . 5 ↑ + j ) - 6 2 / - 0 . 5 ↑ + j ) 0 . 5 α c D ↑ + 7 2 J = - 9 1 - 6 J + 0 . 5 α B e J + α B C ↑ + 1 8 9 - 3 6 J 0 . 5 2 ( ☐ ↑ + 7 2 J = ( 9 + α ☐ c ) ↑ + ( - 4 2 + 0 . 5 ✗ B c ) ; 0 . 5 α C D = 9 + α B C α ( D = 9 + 2 2 8 0 . 5 α C D = 4 7 4 r a d / s ; 7 2 = - 4 2 + 0 . 5 α B C α B C = 7 2 + 4 2 = 2 2 8 r a d / s ² 0 . 5 r , ⇐ , ( r e r i ) ✗ m y = F x m . v n t . I E , r i x m . v e H o = F × M J + H G V c - F a t V I A ; V I V I + T B I C V c = / 0 . 5 0 0 ↑ ) + 1 - 0 . 2 8 7 s i n 3 5 9 + 0 . 2 8 7 c o s 3 5 ° 9 ) = 0 . 3 3 5 ↑ + 0 . 2 3 5 5 W A B = V B / C r B / c → V B / C = W A B ' R B / C ✓ B / c = 1 0 . 9 2 6 r a d s ) / 0 . 1 9 8 m ) = 0 . 1 8 3 m s V B / c = - 0 . 1 8 3 s i n ↑ + 0 . 1 8 3 c o s 3 3 0 J = - 0 . 1 0 5 i n + 0 . 1 0 5 J F B = V 2 + V I C = 1 0 . 3 3 5 9 + 0 . 2 3 5 5 ) + 1 - 0 . 1 0 5 ↑ + 0 . 1 5 0 5 ) T B = ( 0 . 2 1 3 ↑ + 0 . 3 8 5 5 1 m s : V B = 0 . 4 4 8 m / s