Question

An attack helicopter is equipped with a 20- mm cannon that fires 87 g shells in the forward direction with a muzzle speed of 853 m/s. The fully loaded helicopter has a mass of 4410 kg. A burst of 176 shells is fired in a 2.93 s interval. What is the resulting average force on the helicopter?

Answer 1

given,

mass of the shell = 87 g = 0.087 Kg

speed of the muzzle = 853 m/s

mass of the helicopter = 4410 kg

A burst of 176 shell fired in 2.93 s

resulting average force = ?

momentum of the shell = m v

= 0.087 x 853

= 74.21 kgm/s

momentum of 176 shell is = 176 p

= 176 x 74.21

= 13060.96

momentum of helicopter = - 13060.96 kgm/s

amount of speed reduce a =
`(13060.96)/(M)`

a=
`(13060.96)/(4410)`

a = 2.96 m/s²

velocity = \dfrac{2.96}{2.93}

v = 1.01 m/s

Answer 2

4457.7 N

Step-by-step explanation:

87g = 0.087kg

v = 853m/s

t = 2.93 s

total mass hitting = m = 0.087*176 = 15.32 kg

net momentum = mv = 15.32*853 = 13061 kg.m/s

as we know the rate of change of momentum is the average force of impact,

F_avg =
`(mv)/(t)` =
`(13061)/(2.93)` = 4457.7 kg.m/s^2 = 4457.7 N