An airplane, approching an airport for landing, had been asked to wait until the runway is clear. The plane flies a "holding pattern," which basically means it will fly in a circle at a constant height and speed. Suppose the 6.000×104 kg airplane has a speed of 590. km/h and needs to fly in a circle with a radius of 5.95 km. To turn, it will bank (tilt) its wings at some angle; this makes the aerodynamic lift force [(L)\vec] point up and to the left as shown below. What is the magnitude of the lift force on the plane as it travels in this circle?
Question
An airplane, approching an airport for landing, had been asked to wait until the runway is clear. The plane flies a "holding pattern," which basically means it will fly in a circle at a constant height and speed. Suppose the 6.000×104 kg airplane has a speed of 590. km/h and needs to fly in a circle with a radius of 5.95 km. To turn, it will bank (tilt) its wings at some angle; this makes the aerodynamic lift force [(L)\vec] point up and to the left as shown below. What is the magnitude of the lift force on the plane as it travels in this circle?
Solution
To solve this problem, we need to use the formula for centripetal force, which is F = mv^2/r, where m is the mass of the airplane, v is its speed, and r is the radius of the circle it's flying in.
First, we need to convert the speed of the airplane from km/h to m/s, because the units of the other quantities in the formula are in kg and m.
590 km/h = 590,000 m/3600 s = 163.89 m/s
Next, we substitute the given values into the formula:
F = (6.000×10^4 kg) * (163.89 m/s)^2 / 5.95 km = (6.000×10^4 kg) * (163.89 m/s)^2 / 5950 m
Calculating the above expression gives us the magnitude of the lift force on the plane as it travels in this circle.
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