An attack helicopter is equipped with a 20
mm cannon that fires 116 g shells in the
forward direction with a muzzle speed of
819 m/s. The fully loaded helicopter has a
mass of 4870 kg. A burst of 96.2 shells is fired
in a 4.51 s interval.
What is the resulting average force on the
helicopter?
Answer in units of N
By what amount is its forward speed reduced?
Answer in units of m/s
How do i find the amount that the forward speed is reduced once i find the resulting average force on the helicopter?(2026.47113082N)
The amount that the forward speed is reduced can be calculated using the equation F = ma, where F is the force, m is the mass of the helicopter, and a is the acceleration. Rearranging this equation, we get a = F/m. Plugging in the values for F (2026.47113082N) and m (4870 kg), we get a = 0.415 m/s^2. This is the acceleration of the helicopter due to the force of the cannon fire. To find the amount that the forward speed is reduced, we can use the equation vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time interval. Plugging in the values for vi (819 m/s), a (0.415 m/s^2), and t (4.51 s), we get vf = 819 m/s - 1.845 m/s = 817.155 m/s. Therefore, the forward speed of the helicopter is reduced by 1.845 m/s.
Well, that's a rather explosive question, but let me see if I can help you out. To find the resulting average force on the helicopter, we can use Newton's second law, which states that force is equal to mass times acceleration. Rearranging the equation, we have acceleration equals force divided by mass.
First, let's find the acceleration caused by the firing of the shells. To do this, we need to find the change in momentum of the shells, which is mass times change in velocity. The change in velocity is the muzzle speed of the shells, which is 819 m/s.
Change in momentum of shells = (muzzle speed) * (mass of shells) = 819 m/s * (116 g) = 819 m/s * 0.116 kg = 95.004 kg·m/s
Now, we can use this change in momentum to find the resulting average force on the helicopter. Since the burst of 96.2 shells is fired in a 4.51 s interval, we can calculate the average force by dividing the change in momentum by the time interval.
Resulting average force = (change in momentum) / (time interval) = 95.004 kg·m/s / 4.51 s ≈ 21.059 N (rounded to the nearest hundredth)
So, the resulting average force on the helicopter is approximately 21.059 Newtons.
Now, to find the amount by which the helicopter's forward speed is reduced, we need to calculate the acceleration of the helicopter using the same equation as before: force divided by mass.
Acceleration of the helicopter = (resulting average force) / (mass of the helicopter) = 21.059 N / 4870 kg ≈ 0.00432 m/s² (rounded to the nearest ten-thousandth)
Since the time interval in which the burst of shells is fired is 4.51 seconds, we can use this acceleration and the time interval to find the delta-v (change in velocity) of the helicopter.
Delta-v = (acceleration) * (time interval) = 0.00432 m/s² * 4.51 s ≈ 0.01949 m/s (rounded to the nearest hundred-thousandth)
So, the forward speed of the helicopter is reduced by approximately 0.01949 meters per second.
I hope that answers your question, even if it involves an explosive reduction in velocity!
To find the resulting average force on the helicopter, you can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a). In this case, we need to calculate the change in velocity, which will give us the acceleration.
Step 1: Calculate the initial velocity (v1) of the helicopter.
Given:
- Mass of the fully loaded helicopter (m) = 4870 kg
- Muzzle speed of the cannon (v) = 819 m/s
The momentum of the helicopter before firing the shells is given by the formula:
Momentum = mass × velocity
The initial momentum of the helicopter (p1) is equal to its mass multiplied by its initial velocity:
p1 = m × v1
Since the helicopter is initially at rest, the initial velocity is 0.
Therefore, p1 = m × v1 = 4870 kg × 0 = 0 kg·m/s
Step 2: Calculate the final velocity (v2) of the helicopter.
To calculate the final velocity, we need to take into account the recoil caused by firing the shells. This recoil imparts an equal and opposite momentum to the helicopter.
According to the conservation of momentum:
Initial momentum (p1) = Final momentum (p2)
Since the final velocity of the shells (v_shells) is given as 819 m/s, the final momentum of the shells (p_shells) can be calculated as:
p_shells = mass of shells × final velocity of shells
Given:
- Mass of shells (m_shells) = 116 g = 0.116 kg
- Final velocity of shells (v_shells) = 819 m/s
p_shells = m_shells × v_shells = 0.116 kg × 819 m/s
Now, the final momentum of the helicopter (p_helicopter) should be equal in magnitude but opposite in direction to p_shells:
p_helicopter = - p_shells
Therefore:
- p_shells = - p_helicopter
- (0.116 kg × 819 m/s) = - p_helicopter
Step 3: Calculate the change in momentum (Δp) and the average force (F) on the helicopter.
The change in momentum of the helicopter (Δp) is given by:
Δp = p_helicopter - p1
The average force on the helicopter (F) can be calculated using the equation:
F = Δp / t
Given:
- Number of shells fired (n) = 96.2
- Time interval (t) = 4.51 s
Substituting the values:
F = (Δp) / t = (p_helicopter - p1) / t
Now you can calculate the resulting average force and the change in forward speed using the given information and the formulas provided.
To find the resulting average force on the helicopter, you can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a). In this case, the acceleration can be calculated using the change in velocity.
1. First, you need to find the change in velocity caused by firing the burst of shells. This can be calculated using the principle of conservation of momentum.
The momentum change (Δp) is equal to the mass of the shells (m_shell) multiplied by the change in velocity (Δv):
Δp = m_shell * Δv
Given that the mass of each shell is 116 g (or 0.116 kg) and a burst of 96.2 shells is fired, the total mass of the shells is:
m_shell = total shells fired * mass of each shell
m_shell = 96.2 * 0.116 kg
2. Next, you need to find the change in velocity (Δv). This can be calculated using the equation:
Δv = F * Δt / m_helicopter
where F is the resulting average force on the helicopter, Δt is the time interval in which the burst of shells is fired, and m_helicopter is the mass of the helicopter.
Given that the time interval is 4.51 s and the mass of the helicopter is 4870 kg, you can rearrange the equation to solve for F:
F = Δv * m_helicopter / Δt
Plug in the values to calculate the force:
F = (Δp * m_helicopter) / (m_shell * Δt)
Now you can substitute the known values into the equation:
F = (96.2 * 0.116 kg * 4870 kg) / (0.116 kg * 4.51 s)
Simplify the equation:
F = 561966.4 kg kg / s
F = 561966.4 N
Therefore, the resulting average force on the helicopter is approximately 561966.4 N.
To find the amount by which the forward speed is reduced, you can use the equation for average force:
F = Δp / Δt
Rearranging the equation, we have:
Δp = F * Δt
Given that the mass of the shells is 0.116 kg and a burst of 96.2 shells is fired, the total change in momentum (Δp) is:
Δp = m_shell * total shells fired
Substituting the values:
Δp = 0.116 kg * 96.2 shells
To find the change in velocity (Δv), divide Δp by the mass of the helicopter (m_helicopter):
Δv = Δp / m_helicopter
Substituting the known values:
Δv = (0.116 kg * 96.2 shells) / 4870 kg
Simplify the equation:
Δv = 0.002314 kg shells / kg
Therefore, the forward speed is reduced by approximately 0.002314 m/s.