How does the kinetic energy of a moving object change if its momentum is halved

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Solution

Dear Student ,
$T h e r e l a t i o n b e t w e e n k i n e t i c e n e r g y a n d m o m e n t u m o f a n o b j e c t i s : K = \frac{p^{2}}{2 m} w h e r e K i s k i n e t i c e n e r g y, p, i s m o m e n t u m, a n d m i s m a s s . S o, i f t h e m o m e n t u m i s h a l v e d . K' = \frac{p'^{2}}{2 m} = \frac{\frac{p^{2}}{4}}{2 m} = \frac{1}{4} \frac{p^{2}}{2 m} = \frac{1}{4} K S o w h e n p i s h a l v e d, t h e k i n e t i c e n e r g y b e c o m e s o n e f o u r t h o f i t s i n i t i a l .$

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