Calculating Impact Force for Aircraft Landing on Carrier Ship

[codywookman]

Homework Statement

An aircraft is landing on a carrier ship in the middle of the Pacific. When the aircraft’s jump cable catches to stop the plane, the aircraft is traveling at 110 mph with the front of the plane 3 feet off the deck of the ship. If the assumption is made that the cable stops the aircraft immediately (the cable is not elastic), what would be the estimated impact force on the front end of the aircraft with the following conditions?
-The aircraft is 24 feet long
-1000 lbs located 4 feet above rear axle (pivot point)
-5000 lbs located 5 feet above center of plant (when plane is level)
-1500 lbs located 3 feet above front axle
-Do NOT ignore gravity
-Assume no impact absorbed by the front tire

Homework Equations

L (linear momentum) = mass * velocity
A (angular momentum) = L x r (cross product of linear momentum and vector)
kinetic energy ? possible needed

The Attempt at a Solution

Tried using angular momentum (lb ft2 / sec) but that will not add with gravitational force multiplied by distance and mass (lb ft2 / s2). I'm really stuck here please help!

 

[KataKoniK]

Thank you for your post. I am a scientist and I would be happy to assist you in finding a solution to your problem.

First, let's define some variables for easier understanding:

v = velocity of the aircraft (110 mph)
d = distance of the front of the plane from the deck of the ship (3 feet)
L = length of the aircraft (24 feet)
m1 = mass of the aircraft (unknown)
m2 = mass of the 1000 lbs load (1000 lbs)
m3 = mass of the 5000 lbs load (5000 lbs)
m4 = mass of the 1500 lbs load (1500 lbs)
r1 = distance of the 1000 lbs load from the pivot point (4 feet)
r2 = distance of the 5000 lbs load from the pivot point (5 feet)
r3 = distance of the 1500 lbs load from the pivot point (3 feet)
g = acceleration due to gravity (9.8 m/s^2 or 32.2 ft/s^2)

To calculate the estimated impact force, we need to use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the acceleration is given by the change in velocity, which is 110 mph or 161.3 ft/s, over the time it takes for the aircraft to come to a stop. Since we are assuming that the cable stops the aircraft immediately, the time is very small and can be ignored. Therefore, the acceleration is 161.3 ft/s^2.

We can now calculate the linear momentum of the aircraft using the equation L = mv. The linear momentum is a vector quantity, so we need to consider both the magnitude and direction. In this case, the direction of the linear momentum is opposite to the direction of the velocity, so we need to use a negative sign. The linear momentum of the aircraft is therefore given by:

L = -mv = -(m1)(161.3 ft/s)

Next, we need to calculate the angular momentum of the aircraft. Since the aircraft is rotating around a pivot point (the rear axle), we need to use the equation A = L x r, where A is the angular momentum, L is the linear momentum, and r is the distance from the pivot point. The angular momentum is also a vector quantity, so we need to consider both the magnitude

 

[Mene]

I would approach this problem by first breaking it down into smaller, more manageable parts. First, I would calculate the linear momentum of the aircraft using the given mass (in this case, the total mass would be 7500 lbs) and velocity (110 mph). This would give me a value in lb ft/s.

Next, I would calculate the angular momentum of the aircraft using the given mass and distance from the pivot point (in this case, the rear axle). This would give me a value in lb ft2/s.

To determine the impact force, I would then need to consider the kinetic energy of the aircraft, which is calculated using the formula KE = 1/2 * mass * velocity^2. Since the cable stops the aircraft immediately, we can assume that all of its kinetic energy is converted into impact force.

Finally, I would add the linear momentum and angular momentum values together, and then add the calculated kinetic energy to get the total impact force. This would give me a value in lbs, which is the unit of force.

It's important to note that this calculation is an estimate, as it does not take into account any other factors such as air resistance or the elasticity of the cable. However, it can still provide a general idea of the impact force on the front end of the aircraft during landing on the carrier ship.