Airplane (was: Moving Bullet)

In summary, the conversation discusses the problem of finding the mass and distance traveled of a Lufthansa A320 plane as it accelerates from rest to lift-off speed in 25 seconds. It includes the governing equations and the attempt at solving the problem, with the final answer being a mass of 70557.61063kg and a distance traveled of 912.375m.
  • #1
Cole07
106
0

Homework Statement



A Lufthansa A320 accelerates from rest to lift-off speed of 72.99 m/s in 25.00 s. Each of the plane's two jet engines provides a forward force (thrust) of 103.00 kN. What is the mass of the plane?

How far does it travel down the runway before lift-off?

2. Governing equations
Vf=Vi+at
EF=ma
D=Vit+at^2

The Attempt at a Solution


Vf=72.99
Vi=0
a=?
t=25.00s
I used Vf=Vi+at to get a=2.9196
then EF=ma to solve for mass and got 35.27880532 which i was told was wrong i went back and looked at the problem and thought that since the plane has two engines i would double the mass, but it was still wrong. and i tried D=Vit+at^2 for the second problem, but it didn't work either i don't understand what I'm doing wrong. any help would be appreciated
 
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  • #2
Cole07 said:

The Attempt at a Solution


Vf=72.99
Vi=0
a=?
t=25.00s
I used Vf=Vi+at to get a=2.9196
So far, so good. (Don't forget units.)
then EF=ma to solve for mass and got 35.27880532 which i was told was wrong i went back and looked at the problem and thought that since the plane has two engines i would double the mass, but it was still wrong.
F = ma is the right approach. But what's the total F? There are two engines, each giving their own force. And be careful with units: 1 kN = 1 kilo-N = 1000 N.
 
  • #3
I think it should read like this:

103kN x 2 = 206kN
206kN = 206000 Newtons (N)

F=ma

206000 N = (m) (2.9196 m/s^2)

m = 206000 N / 2.9196 m/s^2
 
  • #4
ok i got the mass of the plane to be 70557.61063kg, but i still don't know what I'm doing wrong to get the distance traveled down the runway.
 
  • #5
d = (1/2)(vi + vf)(t)
 
  • #6
i got it 912.375m thank you!
 
  • #7
Cole07 said:
ok i got the mass of the plane to be 70557.61063kg, but i still don't know what I'm doing wrong to get the distance traveled down the runway.

You had a mistake in your distance equation:
D=Vit+at^2
That should be D = Vit + 0.5at^2.
 

What is the concept behind an airplane?

An airplane uses principles of aerodynamics to create lift and propel itself through the air. It has wings that are shaped to create a difference in air pressure, allowing it to fly.

How does an airplane stay in the air?

As an airplane moves forward, its wings create lift by deflecting air downwards. This lift counteracts the force of gravity, allowing the plane to stay in the air.

How do airplanes change direction?

Airplanes use ailerons, elevators, and rudder to change direction. Ailerons control the roll of the plane, elevators control the pitch, and the rudder controls the yaw.

What powers an airplane?

Most airplanes are powered by jet engines, which use the burning of fuel to create propulsion. Some smaller planes use propellers, which are turned by a motor or engine.

What are some safety measures in place for airplanes?

Airplanes undergo regular maintenance checks to ensure they are in proper working condition. They also have safety equipment such as airbags, emergency exits, and flotation devices in case of an emergency.

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