PhysicsLAB AP Free Response Question
2003 Form B - B1

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An airplane accelerates uniformly from rest. A physicist passenger holds up a thin string of negligible mass to which she has tied her ring, which has a mass m. She notices that as the plane accelerates down the runway, the string makes an angle with the vertical as shown above.
(a) In the space below, draw a free-body diagram of the ring, showing and labeling all the forces present.

The plane reaches a takeoff speed of 65 m/sec after accelerating for a total of 30 seconds.
 (b) Determine the minimum length of the runway needed.

 (c) Determine the angle that the string makes with the vertical during the acceleration of the plane before it leaves the ground.

 (d) What additional information would be needed in order to estimate the mechanical energy of the airplane at the instant of takeoff? Explain your answer.

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