# Horizontal acceleration of an aircraft

## 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 [Broken]

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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## Answers and Replies

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.

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 $$\vec{T}$$ (tension in the string) and $$\vec{F_g}=(mg) sin \theta$$ (gravitational force), right? But I don't know what the mass is! How do I need to use your formula without mass?

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.

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?

A diagram says a thousand words! Does this help? The vertical component balances the weight of the mass.
The horizontal component accelerates it with the plane's acceleration.

Yes, it helped a lot. Thank you very much! 