How Do You Calculate the Mass and Runway Distance for a Lufthansa A320?

[Cole07]

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

 

[Doc Al]

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.

 

[ND3G]

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

 

[Cole07]

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.

 

[ND3G]

d = (1/2)(vi + vf)(t)

 

[Cole07]

i got it 912.375m thank you!

 

[Doc Al]

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.