A plane weighing 220 kN (25 tons) lands on an aircraft carrier. The plane is mov

Question

A plane weighing 220 kN (25 tons) lands on an aircraft carrier. The plane is moving horizontally at 67 m/s (150 mi/h) when its tailhook grabs hold of the arresting cables. The cables bring the plane to a stop in a distance of 84 m. (a) How much work is done on the plane by the arresting cables? (b) What is the force (assumed constant) exerted on the plane by the cables? (Both answers will be underestimates, since the plane lands with the engines full throttle forward; in case the tailhook fails to grab hold of the cables, the pilot must be ready for immediate takeoff.)

Explanation / Answer

a) use the work energy theorem and realize that the work done is the change in kinetic energy; the initial kinetic energy of the plane is 1/2 mv^2 and its final KE is zero, so the change in KE = 1/2 mv^2 we are given the weight of the plane as 2.2x10^5N, we divide by g to get its mass of 2.24 x10^4 kg its KE is then 1/2 2.24x10^4 kg x 67^2 = 5.03x10^7 J b) work = force x distance the stopping distance is 84 m, so the average force is f=5.03x10^7J/84 m = 5.98x10^5 N

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