An empty airplane with a mass of 200,000 kg must have a speed of 82 m/s to achieve takeoff. Once it is fully loaded, the airplane has a mass of 350,000 kg. It has 3200 m of runway. a) How much force is needed to get the full airplane safely in the air? b) How much runway would the empty airplane use if its engines generated the same force?
Answers: 3
(1)
- Minimum net force, measured in newtons.
- Runway length, measured in meters. 
- Mass of the airplane, measured in kilograms. 
, 
- Initial and final speeds of the airplane, measured in meters per second.
, 
, 
and 
, then the minimum net force needed by the airplane to get itself safely in the air:
![F = \frac{(350000\,kg)\cdot \left[\left(82\,\frac{m}{s} \right)^{2}-\left(0\,\frac{m}{s} \right)^{2}\right]}{2\cdot (3200\,m)}](/tpl/images/1042/2469/ed7cc.png)
, 
![\Delta s = \frac{(200000\,kg)\cdot \left[\left(82\,\frac{m}{s} \right)^{2}-\left(0\,\frac{m}{s} \right)^{2}\right]}{2\cdot (367718.75\,N)}](/tpl/images/1042/2469/725ed.png)
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