Aircraft runway question - Acceleration, Time and Final Velocity

[Molly1235]

Question:

An aircraft of total mass 1.5 x 10^5kg accelerates at maximum thrust, from rest along a runway for 25s reaching the required take off speed of 65 ms^-1.

Assume that the acceleration of the aircraft is constant. Calculate the distance traveled in this time.

My attempt:

I know s = ((u+v)/2) x t
So I did 65/2 x 25 = 812.5m but u feel like this is too simple and acceleration should be involved here because it's given me the mass of the aircraft?

Any advice?

Many thanks!
Molly

 

[mfb]

Your result is right. If there is no additional question, you don't need the mass of the aircraft.

 

[CWatters]

I get same answer as you.

It's constant acceleration so the SUVAT equations of motions can be used...

http://en.wikipedia.org/wiki/Equations_of_motion#SUVAT_equations

One of those is the equation you used.

Perhaps the mass was given for another part of the question? Do they ask you to calculate the thrust?

 

[Molly1235]

I get same answer as you.

It's constant acceleration so the SUVAT equations of motions can be used...

http://en.wikipedia.org/wiki/Equations_of_motion#SUVAT_equations


One of those is the equation you used.

Perhaps the mass was given for another part of the question? Do they ask you to calculate the thrust?

Well there's another that asks of the length of the runway decreases, what should be changed to enable the aircraft to meet the same take off speed? The only thing I can think of is acceleration...

 

[Molly1235]

Your result is right. If there is no additional question, you don't need the mass of the aircraft.

Ah excellent! Thank you - I just quoted someone else with the sub question...think this may have something to do with the mass...

 

[PhanthomJay]

Well there's another that asks of the length of the runway decreases, what should be changed to enable the aircraft to meet the same take off speed? The only thing I can think of is acceleration...

Yes, and how would you change the acceleration??

...think this may have something to do with the mass...

Yes, but what?

 

[Molly1235]

Yes, and how would you change the acceleration??

Yes, but what?

Would you have to increase the mass in order to increase the acceleration??

 

[mfb]

Would you have to increase the mass in order to increase the acceleration??

Is it easier to push a car, or to push a small stone?
Which one has a larger mass?

 

[CWatters]

Hints:

* The maximum thrust (a.k.a. force) that the engine can produce is fixed.
* The mass of the plane includes the variable mass of the passengers & baggage and fuel.
* Newtons Second law (google it)

 

[Molly1235]

Is it easier to push a car, or to push a small stone?
Which one has a larger mass?

Obviously a stone...so you'd decrease the mass? Acceleration = force/mass and force is fixed, so yeah! Smaller mass = larger acceleration! I think I understand now, thank you!

 

[CWatters]

At some airports in developing countries they can't take off at maximum weight (particularly when its hot and/or the runway is at high altitude). They either have to leave some passengers & baggage behind or take less fuel to reduce weight and plan a stop somewhere to refuel.