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Momentum

a light body ...

Question

a light body and a heavy have same momentum. which one has more kinetic energy

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Solution

$T h e f o r m u l a f o r k i n e t i c e n e r g y i s, K . E . = \frac{1}{2} m v^{2} = \frac{p^{2}}{2 m} . S i n c e t h e m o m e n t a o f t h e t w o b o d i e s a r e t h e s a m e, s o k i n e t i c e n e r g y i s n o w i n f l u e n c e d b y t h e m a s s e s o f t h e t w o b o d i e s, o n e l i g h t e r a n d o t h e r h e a v i e r . K i n e t i c e n e r g y i s i n v e r s e l y p r o p o r t i o n a l t o t h e m a s s o f t h e b o d y i n m o t i o n, s o l i g h t e r b o d y w i l l h a v e m o r e K . E . t h a n h e a v i e r b o d y .$

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