Horizontal acceleration of an aircraft

In summary, the Physics student measures the maximum horizontal acceleration of an aircraft and finds that the maximum acceleration is 2.44 g's.
  • #1
roam
1,271
12

Homework Statement



A Physics student wishes to measure the maximum horizontal acceleration of an aircraft as it accelerates down the runway. To do this the student measures the angle that a weight on a string is deflected from the vertical direction when the plane accelerates (see diagram). If the weight is deflected by a maximum of 14.0° from the vertical what is the maximum acceleration of the plane?

[PLAIN]http://img26.imageshack.us/img26/6634/figurec.gif

The correct answer is 2.44.

The Attempt at a Solution



The only data I'm given is the angle! I don't know at all how to approach this problem... any guidance is very appreciated.
 
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  • #2
Start by identifying the two forces acting on the mass, and which one is causing the mass to accelerate horizontally with the aircraft.

Then consider the other force acting, and use an equation containing it, to give you 2 equations which, hopefully, will allow you to find the acceleration.

Hint: f=ma for the mass to find its (and the plane's) acceleration.
 
  • #3
Stonebridge said:
Start by identifying the two forces acting on the mass, and which one is causing the mass to accelerate horizontally with the aircraft.

Then consider the other force acting, and use an equation containing it, to give you 2 equations which, hopefully, will allow you to find the acceleration.

Hint: f=ma for the mass to find its (and the plane's) acceleration.

The two forces are [tex]\vec{T}[/tex] (tension in the string) and [tex]\vec{F_g}=(mg) sin \theta[/tex] (gravitational force), right? But I don't know what the mass is! How do I need to use your formula without mass?
 
  • #4
Take the horizontal component of the tension as the accelerating force.
Take the vertical component of the tension as equal to the weight of the mass as there is no vertical acceleration.
Eliminate T from those two. m will also disappear.
 
  • #5
Stonebridge said:
Take the horizontal component of the tension as the accelerating force.
Take the vertical component of the tension as equal to the weight of the mass as there is no vertical acceleration.
Eliminate T from those two. m will also disappear.

I'm a little bit confused... what do you mean by the vertical and horizontal components of the tension? Which ones are you reffering to?
 
  • #6
A diagram says a thousand words! Does this help?

figurec.gif


The vertical component balances the weight of the mass.
The horizontal component accelerates it with the plane's acceleration.
 
  • #7
Yes, it helped a lot. Thank you very much! :smile:
 

Related to Horizontal acceleration of an aircraft

1. What is horizontal acceleration in an aircraft?

Horizontal acceleration in an aircraft refers to the change in velocity of the aircraft in the horizontal direction. It is measured in meters per second squared (m/s^2) and is affected by various factors such as the thrust of the engines, air resistance, and the weight of the aircraft.

2. How is horizontal acceleration calculated in an aircraft?

Horizontal acceleration can be calculated by dividing the change in velocity by the time taken for that change to occur. It can also be calculated by using the equation a = F/m, where a is the acceleration, F is the force acting on the aircraft, and m is the mass of the aircraft.

3. What is the role of horizontal acceleration in an aircraft?

Horizontal acceleration is essential for an aircraft to maintain its speed and direction during flight. It allows the aircraft to overcome air resistance and maintain a constant velocity, as well as change its direction when necessary.

4. How does horizontal acceleration affect the passengers on an aircraft?

Horizontal acceleration can cause the passengers to feel a sensation of being pushed back or pulled forward, depending on the direction of acceleration. This is due to the inertia of their bodies, which resists the change in velocity. If the acceleration is too high, it can also cause discomfort or nausea in some passengers.

5. How is horizontal acceleration controlled in an aircraft?

Horizontal acceleration is primarily controlled by the pilot through the use of the aircraft's control surfaces, such as the ailerons and elevators. These surfaces allow the pilot to adjust the aircraft's lift and drag, which in turn affects the horizontal acceleration. The pilot can also adjust the thrust of the engines to control the horizontal acceleration of the aircraft.

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