An attack helicopter is equipped with a 20-
mm cannon that fires 105 g shells in the
forward direction with a muzzle speed of
669 m/s. The fully loaded helicopter has a
mass of 4260 kg. A burst of 133 shells is fired
in a 5.41s interval.
What is the resulting average force on the
helicopter?
By what amount is its forward speed reduced?
force*time=massbullets*velocity
force=massbullets/time * velocity
but the massbullets/time=133*.105/5.41
solve for force.
To find the resulting average force on the helicopter, we can use the principle of conservation of momentum. The momentum before the burst equals the momentum after the burst.
The momentum before the burst is given by the mass of the helicopter multiplied by its initial velocity:
Initial momentum = Mass × Initial velocity
= 4260 kg × 669 m/s
The momentum after the burst is the sum of the momentum of the fired shells and the momentum of the helicopter. The momentum of the fired shells is the mass of one shell multiplied by the muzzle speed and the number of shells fired:
Momentum of the fired shells = mass of one shell × muzzle speed × number of shells fired
= 105 g × 0.105 kg/g × 669 m/s × 133 shells
The final momentum of the helicopter is the mass of the helicopter multiplied by its final velocity. Since the helicopter is at rest after the burst, its final velocity is 0 m/s.
Final momentum = Mass × Final velocity
= 4260 kg × 0 m/s
= 0 kg•m/s
Using the principle of conservation of momentum, we have:
Initial momentum = Momentum of the fired shells + Final momentum
4260 kg × 669 m/s = 105 g × 0.105 kg/g × 669 m/s × 133 shells + 0 kg•m/s
Now, let's solve for the resulting average force on the helicopter.
Average force = Change in momentum / Change in time
Change in momentum = Final momentum - Initial momentum
= 105 g × 0.105 kg/g × 669 m/s × 133 shells - (4260 kg × 669 m/s)
Change in time = 5.41 s
Finally, we can calculate the resulting average force on the helicopter:
Average force = (105 g × 0.105 kg/g × 669 m/s × 133 shells - (4260 kg × 669 m/s)) / 5.41 s
To find the amount by which the forward speed is reduced, we can use the concept of impulse. The impulse on the helicopter is equal to the change in momentum. Since the momentum before the burst is the same as the momentum after the burst, the impulse is equal to zero. Therefore, the forward speed of the helicopter is not reduced.
Note: Please note that the assumptions made for simplicity in this calculation may not accurately represent real-life situations.
To find the resulting average force on the helicopter, we need to use the principle of impulse-momentum. The impulse experienced by an object is equal to the change in momentum it undergoes. In this case, the change in momentum of the helicopter can be calculated as the sum of the momentum of all the shells fired.
To calculate the change in momentum, we need to know the mass and velocity of each shell. Given that each shell has a mass of 105 g (or 0.105 kg) and a muzzle speed of 669 m/s, we can calculate the initial momentum of each shell using the formula:
Momentum = mass * velocity
So the initial momentum of each shell is 0.105 kg * 669 m/s = 69.945 kg·m/s.
Since 133 shells are fired in a burst, the total initial momentum of all the shells fired is 133 * 69.945 kg·m/s = 9325.085 kg·m/s.
Now let's find the change in momentum of the helicopter. The momentum of the helicopter can be calculated as the product of its mass and its initial velocity. Given that the mass of the fully loaded helicopter is 4260 kg and its initial velocity is unknown, we can use an equation of motion to determine it. Assuming there is no external force except for the force exerted by the fired shells, the initial momentum of the helicopter is zero, so we have:
Momentum = mass * velocity
0 = 4260 kg * velocity
Rearranging the equation, we find that the initial velocity of the helicopter is 0 m/s.
The final momentum of the helicopter can be calculated as the product of its mass and its final velocity. Assuming the forward speed of the helicopter is reduced due to the impulse from the shells, the final velocity of the helicopter is unknown. Again, assuming no external force other than the shell impulse, we have:
Momentum = mass * velocity
Final Momentum = 4260 kg * velocity
Now, using the principle of impulse-momentum, we can calculate the change in momentum of the helicopter:
Change in Momentum = Final Momentum - Initial Momentum
Change in Momentum = (4260 kg * velocity) - 0 kg·m/s
Change in Momentum = 4260 kg·m/s * velocity
Now, equating the change in momentum to the total initial momentum of the shells, we have:
Change in Momentum = Total Initial Momentum of Shells
4260 kg·m/s * velocity = 9325.085 kg·m/s
Simplifying the equation, we find:
velocity = 9325.085 kg·m/s / 4260 kg
velocity ≈ 2.185 m/s
So, the forward speed of the helicopter is reduced by about 2.185 m/s due to the impulse from the shells.
To find the resulting average force on the helicopter, we can use the formula for force:
Force = Change in Momentum / Time Interval
Force = (4260 kg·m/s * 2.185 m/s) / 5.41 s
Calculating the force, we find:
Force ≈ 1735.628 N
Therefore, the resulting average force on the helicopter is approximately 1735.628 N.