question number 33

Asked by neha14072006 | 21st Jun, 2020, 08:15: PM

Expert Answer:

Question: - A gun of mass 3 kg fires a bullet of mass 30 g. The bullet takes 0.003s to move through the barrel of the gun and acquires a velocity of 100 m/s.
Calculate:(i) the velocity with which the gun recoils
(ii) the force exerted on gunman due to recoil of the gun. 
 
Solution: - 
M a s s space o f space g u n comma space M space space equals space 3 space k g space
m a s s space o f space b u l l e t comma m space equals space 30 space g space equals space 0.03 space k g space
i n i t i a l space v e l o c i t y space o f space b u l l e t comma space u subscript 1 space equals space 0 space m divided by s
f i n a l space v e l o c i t y space o f space b u l l e t comma space v subscript 1 space equals space 100 space m divided by s
I n i t i a l space v e l o c i t y space o f space g u n comma space u subscript 2 space equals space 0 space m divided by s space
F i n a l space v e l o c i t y space o r space r e c o i l space v e l o c i t y space o f space g u n comma space v subscript 2 space equals space ?
A p p l y i n g space l a w space o f space c o n s e r v a t i o n space o f space m o m e n t u m comma space
I n i t i a l space m o m e n t u m space equals space F i n a l space m o m e n t u m space
m u subscript 1 space plus space M u subscript 2 space equals space m v subscript 1 space plus space M v subscript 2 space
0 space equals space 0.03 space cross times 100 space plus thin space 3 cross times v subscript 2 space
v subscript 2 equals space minus fraction numerator space 0.03 space cross times 100 space over denominator 3 end fraction space equals space minus 1 space m divided by s

T h u s comma space r e c o i l space v e l o c i y y space o f space g u n space i s space 1 space m divided by s
N e g a t i v e space s i g n space i n d i c a t e s space t h a t space t h e space g u n space m o v e s space i n space d i r e c t i o n space o p p o s i t e space t o space t h a t space o f space b u l l e t space
N o w space l e t apostrophe s space c a l c u l a t e space t h e space f o r c e space e x e r t e d space o n space g u n comma space
F space space equals space m a
a space equals space fraction numerator v space minus space u space over denominator t end fraction
T h u s comma space
F space equals space M space fraction numerator left parenthesis v subscript 2 space minus space u subscript 2 right parenthesis over denominator t end fraction equals space fraction numerator 3 left parenthesis negative 1 right parenthesis over denominator 0.003 end fraction space equals space minus 1000 space N space

Answered by Shiwani Sawant | 22nd Jun, 2020, 03:26: PM