# Q & A: Newton’s Second Law and Airplanes

Q:
According to the equation F=ma, if the mass is smaller, then the acceleration will be stronger. Why does this cause smaller airplanes to fly farther than larger airplanes? Does acceleration affect how long an airplane can stay in the air?
- Maggie (age 15)
Pennsylvania, USA
A:
Yes, if the same amount of force is applied to two objects, then the lighter one will accelerate faster, according to Newton's Second Law, F=ma. Here, F is the sum of all forces on the object. For an airplane, there are four forces involved:
• weight -- gravity pulls down.
• lift -- airflow past the wings generates an upward force.
• drag -- airflow past the airplane pushes back on the airplane and slows it down
• thrust -- jet or propellor engines push the airplane forwards
Typically, airplanes which fly long distances, like commercial passenger aircraft, do so at more or less constant speeds over most of the journey. So the acceleration is zero most of the time! Fuel must still be burned to overcome drag and to redirect airflow to generate lift. How far an airplane (with an engine) flies depends on how much fuel it can carry, and how heavy it is (and on things like its wing design). A heavy airplane must constantly expend energy pushing through the air, directing airflow downwards to push itself up so it doesn't fall.

If the airplane doesn't have an engine (such as a paper airplane), then it will travel farther and stay aloft longer if it starts out faster. But a very light paper airplane has a problem with drag -- if the airplane is very light, it doesn't take much of a drag force to slow it down.

Tom

(published on 10/22/2007)