Normal force on the landing gear when the airplane lands

[Wapapow10]

Homework Statement

An airplane of mass 25,000 kg (approximately the size of a Boeing 737) is coming in for a landing at a speed of 72 m/s. Calculate the normal force on the landing gear when the airplane lands. Hint: You will use 0.92 m as the compression (vertical displacement) of the landing gear shock absorbers when the plane contacts the ground and 5° as the angle that the landing velocity makes with the horizontal.

Homework Equations

The Attempt at a Solution

plane N 9.8*25000=245000N
a=vf^2-vi^2/2*-.92=36.31m/s
Fn=245000=25000*36.31=664750N*******
dy=-.92
viy=-6.27
vfy=0
a=36.39


Not sure what I am doing wrong

 

[rude man]

When the landing gear first touches the ground, what is the normal velocity? What is the normal kinetic energy? Can you somehow equate that energy with the work the force does as it travels over the 0.92m?

 

[Wapapow10]

I thought that's why I did 0-6.7^2/2*9.2
44.89/1.8=24.93

sorry I had to I was mixing numbers from another question.

 

[rude man]

I can't figure out your numbers since you didn't define where they came from.

I should have added that in addition to the change in kinetic energy of the plane at the beginning and at the end of the 0.92m descent, there is also a loss of potential energy. Both are reduced by the action of the force over the given vertical distance.

 

[HalfLostAndSearching]

, but your attempt at a solution is incorrect. You have correctly calculated the weight of the airplane (245,000 N) and the vertical displacement of the landing gear (0.92 m). However, the acceleration you have calculated (36.31 m/s^2) is incorrect. The correct acceleration should be calculated using the landing velocity (72 m/s) and the angle of descent (5°). This can be done using trigonometry to find the vertical component of the landing velocity, which is the acceleration due to the normal force. Once you have the correct acceleration, you can use Newton's second law (F=ma) to calculate the normal force on the landing gear. Your final answer should be approximately 1,261,115 N.