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Chapter 4: Problem 30

At 560 metric tons, the Airbus \(A-380\) is the world's largest airliner. What's the upward force on an \(A-380\) when the plane is (a) flying at constant altitude and (b) accelerating upward at \(1.1 \mathrm{m} / \mathrm{s}^{2} ?\)

Short Answer

Expert verified
The upward force on the A-380 when the plane is (a) flying at constant altitude is \(5,488,000 \, \mathrm{N}\) and (b) accelerating upward at \(1.1 \, \mathrm{m/s^2}\) is \(6,104,000 \, \mathrm{N}\).

Step by step solution

01

Calculate Force When Flying at Constant Altitude

When the plane is flying at constant altitude, there's no upward acceleration. Hence, the net force equals zero, and the upward force (the lift) equals the force of gravity. Thus, first calculate the force of gravity. The force of gravity equals the mass times the acceleration due to gravity, which is \(9.8 \, \mathrm{m/s^2}\) on earth's surface. Thus, the force of gravity is \(560,000 \, \mathrm{kg} * 9.8 \, \mathrm{m/s^2} = 5,488,000 \, \mathrm{N}\). The lift equals the force of gravity, so the upward force (the lift) on the A-380 when flying at constant altitude is \(5,488,000 \, \mathrm{N}\).
02

Calculate Force When Accelerating Upward

When the plane is accelerating upward, find the net force first. The net force on the A-380 equals the mass times the acceleration. Hence, the net force is \(560,000 \, \mathrm{kg} * 1.1 \, \mathrm{m/s^2} = 616,000 \, \mathrm{N}\). Since the net force equals the lift minus the force of gravity, you can solve for the lift, which is the upward force. Thus, the upward force is \(5,488,000 \, \mathrm{N} + 616,000 \, \mathrm{N} = 6,104,000 \, \mathrm{N}\). This is the upward force on the A-380 when it's accelerating upward at \(1.1 \, \mathrm{m/s^2}\).

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