a machine gun has a mass of 20kg. it fires 30g bullet at the rate of 400 bullets per sec with the speed of 400m/s. what force must be applied to the gun to keep it in position?

Asked by science field | 14th Oct, 2014, 08:05: PM

Expert Answer:

begin mathsize 14px style Mass space of space the space gun comma space straight M equals 20 space Kg comma Mass space of space each space bullet comma space straight m space equals space 30 space straight g equals 0.030 space kg Velocity space of space bullet comma space straight v space equals space 400 space straight m divided by straight s space Number space of space bullets space fired space per space second space space equals space 400 space Let space straight V space be space the space recoil space velocity comma space then space we space can space write space straight V space equals mv over straight M equals fraction numerator 0.030 cross times 400 over denominator 20 end fraction equals 0.6 space straight m divided by straight s Time space taken space to space fire space one space bullet space equals space 1 over 400 sec Let space straight F space be space the space average space force space required space to space hold space the space gun space in space position comma space then straight F space equals fraction numerator Change space in space momentum space of space gun over denominator time end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis Initial space momentum space of space the space gun space is space zero right parenthesis Therefore comma space straight F equals MV over straight t equals fraction numerator 20 cross times 0.6 over denominator 1 divided by 400 end fraction equals 4800 space straight N    end style

Answered by Jyothi Nair | 15th Oct, 2014, 09:48: AM