5 You can use this video to help you httpsyoutube5ltjFEei3AI

5. You can use this video to help you https://youtu.be/5ltjFEei3AI You’re a pilot for the Navy. For your airplane to be able to lift itself off the ground, it must be traveling forward with a speed of 208 km/h (130 mph). a. The force exerted by the air on the airplane causes it to accelerate down the runway. How long must the runway be for the airplane to reach its takeoff speed? b. An aircraft carrier runway is only about 100 m long. As your answer to part b indicates, this distance is not enough for the airplane to reach takeoff speed on its own. The aircraft carrier must assist the airplane by exerting an extra force on it. The aircraft carrier uses a steam-powered catapult to help push the airplane forward. How much additional force must the catapult exert on the airplane to bring the airplane to takeoff speed at the end of the 100-m runway? c. How does a helicopter fly that allows it to land in a smaller space then a jet? d. Why do aircraft carriers use more jets than helicopter? e. What is a sonic boom, and what causes it?

Solution

(a) 200 metres
     The airplane will be able to take off when it is reaches 130 miles-per-hour, at which time it will have 50,000,000 joules of kinetic energy. To give the airplane 50,000,000 joules of kinetic energy, work must be done on it . 50,000,000 joules is 50,000,000 newton-meters. In this case, the force available from the engine is 250,000 newtons so 200 meters is required (250,000 newtons times 200 meters is 50,000,000 newton-meters). The airplane will reach take off energy and speed after 200 meters of accelerating forward in response to the forces from the air leaving its own engines.

(b) 250,000 additional newtons in the forward direction.
To reach take off energy and speed after only 100 meters will require a force of 500,000 newtons. Since 250,000 newtons is available from the air leaving the engines themselves, the catapult must exert an additional 250,000 newton on the plane in the forward direction. If the catapult were required to bring the airplane to take off speed in even less distance, still more force would be required. Below a certain length, the force would have to be so high that it would break the airplane. That explains why airplanes cannot be shot off the carrier deck with explosives, although sometimes rocket packs are used.