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Impulsive Forces in Collision

A particle of...

Question

A particle of mass m is made to move with uniform speed u along the perimeter of a regular polygon of n sides. What is the magnitude of impulse applied by the particle at each corner of the polygon?

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Solution

$I m p u l s e i s a l o n g t h e l i n e j o i n i n g t h e c o r n e r t o t h e c e n t e r o f t h e p o l y g o n . A n g l e b e t w e e n t h e s i d e o f t h e p o l y g o n a n d t h e l i n e j o i n n i n g t h e c e n t e r t o t h e c o r n e r i s \frac{π}{2} - \frac{π}{n} . I m p u l s e = m u c o s (\frac{π}{2} - \frac{π}{n}) - (m u c o s (\frac{π}{2} - \frac{π}{n})) = 2 m u c o s (\frac{π}{2} - \frac{π}{n}) = 2 m u s i n (\frac{π}{n})$

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