An attack helicopter is equipped with a 20-
mm cannon that fires 198 g shells in the
forward direction with a muzzle speed of
711 m/s. The fully loaded helicopter has a
mass of 4810 kg. A burst of 75.3 shells is fired
in a 6.27 s interval.
What is the resulting average force on the
helicopter?
Answer in units of N
The fired shells exert a backward force on the helicopter that equals the rate that forward momentum is created for the shells.
F = (75.3)(0.198)*(711)/6.27 = 1691 N
kg*m/s*(1/s) = Newtons
Well, if an attack helicopter is firing a bunch of shells, I guess it can be called a "firework" helicopter! Now, let's calculate the average force on this explosive chopper.
To find the average force, we need to use Newton's second law, which states that force equals mass times acceleration (F = ma). In this case, the acceleration is the change in velocity over time.
First, let's find the change in velocity of each shell:
Δv = muzzle speed = 711 m/s
Next, we can calculate the total change in momentum:
Δp = (mass of one shell) * (number of shells)
Δp = (0.198 kg) * (75.3 shells)
Since momentum is the product of mass and velocity (p = mv), we can determine the change in velocity by dividing the total change in momentum by the mass of the helicopter:
Δv = Δp / (mass of the helicopter)
Δv = [(0.198 kg) * (75.3 shells)] / (4810 kg)
Now, let's calculate the time interval:
t = 6.27 s
To find the resulting average force, we can use the equation:
average force = total change in momentum / time interval
average force = (Δp / t)
Now, let's plug in the values:
average force = [(0.198 kg) * (75.3 shells)] / (4810 kg * 6.27 s)
Calculating this out will give us the average force on the helicopter. But remember, don't let it "shell-shock" you when you see the answer!
To find the resulting average force on the helicopter, we can use the principle of conservation of momentum. The change in momentum of the helicopter is equal to the impulse experienced by the cannon shells.
First, we need to calculate the initial momentum of the shells. The formula for momentum is given by:
momentum = mass x velocity
The mass of each shell is provided as 198 g, but we need to convert it to kg:
mass = 198 g = 198/1000 kg = 0.198 kg
The initial velocity of the shells is given as 711 m/s.
Now, we can calculate the initial momentum of each shell:
initial momentum of each shell = mass x velocity
= 0.198 kg x 711 m/s
= 140.778 kg·m/s
To find the total initial momentum of the burst of shells, we can multiply the initial momentum of each shell by the number of shells fired:
total initial momentum of burst = initial momentum of each shell x number of shells
= 140.778 kg·m/s x 75.3 shells
Next, we need to calculate the final momentum of the burst of shells. Since the shells are fired in the forward direction, the final momentum will be the same as the total initial momentum.
Now, let's calculate the change in momentum:
change in momentum = final momentum - initial momentum
= total initial momentum
As per the conservation of momentum, the change in momentum experienced by the shells is equal to the change in momentum experienced by the helicopter. Therefore, the resulting average force on the helicopter is equal to the change in momentum divided by the time interval:
average force = change in momentum / time interval
= total initial momentum / time interval
= (140.778 kg·m/s x 75.3 shells) / 6.27 s
= 168066.234 N
Therefore, the resulting average force on the helicopter is 168066.234 N.
To find the resulting average force on the helicopter, we need to use Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum.
First, let's calculate the momentum of each shell. The momentum of an object can be calculated by multiplying its mass by its velocity. In this case, the mass of the shell is 198 g, which is 0.198 kg (since 1 kg = 1000 g), and the velocity is 711 m/s.
Momentum of each shell = Mass of shell × Velocity of shell
= 0.198 kg × 711 m/s
Next, let's calculate the total momentum of 75.3 shells. Since the shells are being fired in a rapid burst, we can assume that the momentum of each shell adds up linearly.
Total momentum of 75.3 shells = Momentum of each shell × Number of shells
= (0.198 kg × 711 m/s) × 75.3
Now, we need to calculate the change in velocity of the helicopter. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Hence, the momentum imparted to the shells will result in an equal and opposite change in momentum for the helicopter. Since the helicopter is initially at rest, the final momentum of the helicopter will be equal to the total momentum of the shells.
Change in momentum of the helicopter = Total momentum of 75.3 shells
Finally, we can calculate the average force on the helicopter by dividing the change in momentum by the time interval during which the shells were fired.
Average force on the helicopter = Change in momentum of the helicopter / Time interval
= (Total momentum of 75.3 shells) / 6.27 s
Plugging in the given values and performing the calculations will give us the resulting average force on the helicopter in units of Newtons (N).