Question-22487

Question Number 22487 by ajfour last updated on 19/Oct/17

Commented by ajfour last updated on 19/Oct/17

Q . 22473 (s o l u t i o n)

Answered by ajfour last updated on 19/Oct/17

\int_{0}^{△ t} f d t = m (u \sin α - v \cos α)

= 0.1 (20 \times \frac{1}{2} - 10 \times \frac{\sqrt{3}}{2})

= (1 - \frac{\sqrt{3}}{2}) N s

\int_{0}^{△ t} N d t = m (u \cos α + v \sin α)

= 0.1 (20 \times \frac{\sqrt{3}}{2} + 10 \times \frac{1}{2})

= \sqrt{3} + \frac{1}{2}

I △ ω = - R \int_{0}^{△ t} f d t

\frac{1}{2} (ω - 2) = - \frac{1}{2} (1 - \frac{\sqrt{3}}{2})

\Rightarrow ω = 2 - 1 + \frac{\sqrt{3}}{2} > 0

\Rightarrow I m m e d i a t e l y a f t e r c o l l i s i o n

{r i n g}^{'} s a n g u l a r v e l o c i t y i s i n t h e

s a m e d i r e c t i o n .

F o r T r a n s l a t o r y m o t i o n : l e t V b e

f i n a l t r a n s l a t i o n a l v e l o c i t y o f

r i n g, t h e n

M (V - v_{0}) = - \int_{0}^{△ t} (f \sin α + N \cos α) d t

2 (V - 1) = - (\frac{1}{2} - \frac{\sqrt{3}}{4} + \frac{3}{2} + \frac{\sqrt{3}}{4})

\Rightarrow 2 V - 2 = - 2 o r V = 0

R i n g s t o p s .

S o i m m e d i a t e l y a f t e r c o l l i s i o n r i n g r o t a t e s

a b o u t s t a t i o n a r y c e n t r e o f m a s s

i n t h e s a m e s e n s e a s b e f o r e o n l y

l i t t l e s l o w e r, f r i c t i o n a c t s l e f t .

L a t e r i t s h o u l d b r i n g r i n g i n t o

p u r e r o l l i n g c o n d i t i o n .

Commented by Sahib singh last updated on 19/Oct/17

T h a n k y o u v e r y m u c h

s i r .