discuss how the principle of conservation of momentum is used in the launching of rockets.deduce an expression for(1)velocity at any instant (2)accerleration of rocket and force experienced

Open in App

Solution

Dear student
$L e t m a s s o f r o c k e t w h e n i t s t a r t s f l y i n g b e M a n d i t s i n i t i a l v e l o c i t y i s u . I f t h e r o c k e t e j e c t s t h e m a s s o f g a s e s a t t h e r a t e o f \frac{d m}{d t} i n t h e d o w n w a r d d i r e c t i o n a n d v e l o c i t y o f e j e c t i o n o f g a s e s r e l a t i v e t o t h e b o d y o f t h e r o c k e t i s v_{r e l a t i v e} = v_{r} . F r o m t h e f r e e b o d y d i a g r a m o f t h e r o c k e t a s s h o w n i n f i g u r e U p t h r u s t a c t i n g o n t h e r o c k e t i s = - v_{r} \times \frac{d m}{d t} (\frac{d m}{d t} i s n e g a t i v e s o m u l t i p l i e d w i t h n e g a t i v e s i g n t o m a k e i t p o s i t i v e) l e t m a s s o f t h e r o c k e t a f t e r a t i m e t o f i t s s t a r t s i s m s o i t s w e i g h t i s = m g a) - v_{r} \times \frac{d m}{d t} - m g = m a (a i s t h e a c c e l e r a t i o n) b) - v_{r} \times \frac{d m}{d t} - m g = m \times \frac{d v}{d t} - v_{r} d m - m g d t = m d v m u l t i p l l y i n g w i t h t h e b o t h s i d e s - v_{r} d m - m g d t = m d v d i v i d i n g b o t h s i d e s w i t h m - v_{r} \times \int_{M}^{m} \frac{d m}{m} - \int_{0}^{t} g d t = \int_{u}^{v} d v - v_{r} \ln (\frac{m}{M}) - g t = v - u v = u - g t - \ln (\frac{m}{M}) v = u - g t + \ln (\frac{M}{m}) R e g a r d s$

Suggest Corrections

Similar questions

Explain how the law of conservation of momentum can be used to explain (i) recoil of a gun (ii) motion of a rocket.

Join BYJU'S Learning Program