Analyzing the motion of an airplane based on design specs of the airplane

[theresa17]

Homework Statement

Calculate the position (distance) and velocity of the plane at 5 equal time intervals based on constant acceleration until the takeoff point. The 5th point should be the takeoff point. Calculate the abort point, if the plane needs to make a sudden stop. Determine the distance to the final stopping point after landing.
FBD: Calculate all of the forces acting on the plane while it is flying at a constant velocity and altitude.
Graphs: Graph velocity of the plane versus time and distance versus time for the 8 time intervals (where in the problem can you infer that there are 8 points?)

Here's what information I have:
Mass of airplane: 1060 kg
Take-off speed: 65 knots--> 33.44 m/s
Engine Thrust: 1500 N
Landing speed: 72 knots--> 37.04 m/s
Maximum abort speed: 58 knots--> 29.834 m/s
FAA noise abatement height for takeoff: 150 m
Breaking coefficient of friction: 0.30
Take off angle: 35 degrees

Runway Design Terms:
Abort velocity- The FAA establishes a point during take off when the pilot must shut down and come to a stop or if the pilot passes this point he/she must take off. The runway must include enough length for the pilot to use reverse engine thrust and braking friction to stop safely if the decision is made not to take off.

Take-off angle- The maximum angle to the horizontal that the pilot can use to gain altitude just after take off.

FAA Noise Abatement- The FAA sets minimum flights standards for planes flying over populated areas. These minimum heights must be met by placing runways far enough from residential areas to allow the planes to meet these standards. Planes normally maintain their take off speeds until the exceed these minimum heights.

Homework Equations

a=$$\Delta$$v/t
vf=vi+at
d=vit+1/2at^2
v=d/t

The Attempt at a Solution

*Units included
This is my attempt at finding the time:
a=$$\Delta$$v/t
9.8m/s/s=3.6/t
t=.3673 s

This is my attempt at finding distance:
d=vit+1/2at^2
d=(33.44m/s)(.3673s)+1/2(9.8m/s/s)(.3673)^2
d=12.94 m

This is my attempt at finding a second distance:
d=(33.44m/s)(.7346s)+1/2(9.8m/s/s)(.7346s)^2
d=27.21m

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This is for my Unit project. Everything in the given section, is what I have been given.
My current grade is a 73%. I try my ABSOLUTE hardest. I do perfectly fine on classwork and homework but bomb tests and quizzes- why, I have NO idea whatsoever.
I really would like to get a good grade on this project. I have calculated 5 distances but I included two because I just want to know if I am on the right track.
I am making an assumption right now that this website is going to become my lifesaver- you truly don't understand how frustrating getting the type of grades I get is for me, when I try my absolute hardest. It's almost like I do everything for nothing.
I try so so hard. I want to do good. I am graduating high school a year early, and physics is bringing my GPA down and it is frustrating me so much.Please please please and thank you thank you thank you in advance!
P.S.- I'm new here and this is my first post, so if something is missing or whatever, don't hurt me, I'm still learning :)

 

[denverdoc]

I can see why it is frustrating. It is a great question,, however.

Thankfully it doesn't involve lift which might do what to the frictional force between the wheels and aircraft?

Ok not mentioned, so just consider the result of ma=Force of acceration - frictional force.

Here friction force is equal to the weight of the aircrafttimes the coefficient of friction.

So you can calulate net force and acceleration from that, and can solve the problem.
Recall V=a*t

 

[kerimek]

Dear student,

First of all, I want to commend you for your hard work and dedication in trying to understand and complete this project. I can understand the frustration of not being able to achieve the grades you desire, even after putting in your best effort. But please remember that grades do not define your intelligence or potential. Keep working hard and never give up.

Now, let's focus on the project. Your attempts at finding time and distance seem to be on the right track. However, there are a few things that need to be clarified and addressed.

Firstly, the given mass of the airplane (1060 kg) is not needed to calculate time or distance. It is only required for calculating forces later on.

Secondly, it is mentioned that the airplane is flying at a constant velocity and altitude, but you have calculated distances as if it is accelerating. This may be a mistake, so please clarify this with your teacher.

Thirdly, it is not mentioned at what speed the airplane is flying at a constant velocity. This information is needed to calculate the distance and time intervals at which the position and velocity need to be calculated.

Fourthly, it is not clear what is meant by "8 time intervals" and where they are mentioned in the problem. Please provide more information on this.

Furthermore, the given equations are correct, but they need to be applied correctly. For example, in your attempt to find time, the acceleration value should be in m/s^2, not m/s/s. Similarly, in your attempt to find distance, the acceleration value should be multiplied by (0.7346s)^2, not (0.7346s). These small mistakes can make a big difference in your final answer.

Lastly, it is not clear what is meant by "breaking coefficient of friction". Is it the coefficient of kinetic friction between the tires of the airplane and the runway? Or is it the coefficient of drag? Please clarify this with your teacher.

In conclusion, please make sure to clarify the above-mentioned points with your teacher and double-check your calculations. Also, try to understand the concepts behind the equations and how they are applied in this problem. If you need further help, don't hesitate to ask your teacher or a tutor for assistance. Keep up the good work and I wish you all the best in your studies.

Sincerely,
A scientist