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An airplane in flight is subject to an air resistance force proportional to the square of its speed v. But there is an additional resistive force because the airplane has wings. Air flowing over the wings is pushed down and slightly forward, so from Newton's third law the air exerts a force on the wings and airplane that is up and slightly backward (Figure 1). The upward force is the lift force that keeps the airplane aloft, and the backward force is called induced drag. At flying speeds, induced drag is inversely proportional to v², so that the total air resistance force can be expressed by Fair=av² + B/v², where a and 3 are positive constants that depend on the shape and size of the airplane and the density of the air. To simulate a Cessna 150, a small single-engine airplane, use a = 0.320 N s²/m² and 3 = 3.59x105 Nm²/s². In steady flight, the engine must provide a forward force that exactly balances the air resistance force. Figure Induced drag Lift Force of air on wings < 1 of 1 > Part A Calculate the speed at which this airplane will have the maximum range (that is, travel the greatest distance) for a given quantity of fuel. Express your answer in meters per second. IVE ΑΣΦ V = Submit ▾ Part B V = Submit Request Answer Calculate the speed for which the airplane will have the maximum endurance (that is, will remain in the air the longest time). Express your answer in meters per second. 15. ΑΣΦΑ Provide Feedback ? Request Answer m/s ? m/s

An airplane in flight is subject to an air resistance force proportional to the square of its speed v. But there is an additional resistive force because the airplane has wings. Air flowing over the wings is pushed down and slightly forward, so from Newton's third law the air exerts a force on the wings and airplane that is up and slightly backward (Figure 1). The upward force is the lift force that keeps the airplane aloft, and the backward force is called induced drag. At flying speeds, induced drag is inversely proportional to v², so that the total air resistance force can be expressed by Fair=av² + B/v², where a and 3 are positive constants that depend on the shape and size of the airplane and the density of the air. To simulate a Cessna 150, a small single-engine airplane, use a = 0.320 N s²/m² and 3 = 3.59x105 Nm²/s². In steady flight, the engine must provide a forward force that exactly balances the air resistance force. Figure Induced drag Lift Force of air on wings < 1 of 1 > Part A Calculate the speed at which this airplane will have the maximum range (that is, travel the greatest distance) for a given quantity of fuel. Express your answer in meters per second. IVE ΑΣΦ V = Submit ▾ Part B V = Submit Request Answer Calculate the speed for which the airplane will have the maximum endurance (that is, will remain in the air the longest time). Express your answer in meters per second. 15. ΑΣΦΑ Provide Feedback ? Request Answer m/s ? m/s

University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter5: Newton's Law Of Motion
Section: Chapter Questions
Problem 89AP: In building a house, carpenters use nails from a large box. The box is suspended from a spring twice...
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An airplane in flight is subject to an air resistance force proportional to the square of its speed v. But there is an additional resistive force because the airplane has wings. Air flowing over the wings is pushed down and slightly forward, so from Newton's third law the air exerts a force on the wings and airplane that is up and slightly backward (Figure 1). The upward force is the lift force that keeps the airplane aloft, and the backward force is called induced drag. At flying speeds, induced drag is inversely proportional to ², so that the total air resistance force can be expressed by Fair = av² + B/v². where a and ß are positive constants that depend on the shape and size of the airplane and the density of the air. To simulate a Cessna 150, a small single-engine airplane, use a = 0.320 N -s²/m² and 3 = 3.59x105 Nm²/s². In steady flight, the engine must provide a forward force that exactly balances the air resistance force. Figure Induced drag Lift Force of air on wings 1 of 1 Part A Calculate the speed at which this airplane will have the maximum range (that is, travel the greatest distance) for a given quantity of fuel. Express your answer in meters per second. VE ΑΣΦΑ V= Submit Part B V= Submit Request Answer Calculate the speed for which the airplane will have the maximum endurance (that is, will remain in the air the longest time). Express your answer in meters per second. ][| ΑΣΦ Provide Feedback ? Request Answer m/s ? m/s
Transcribed Image Text:An airplane in flight is subject to an air resistance force proportional to the square of its speed v. But there is an additional resistive force because the airplane has wings. Air flowing over the wings is pushed down and slightly forward, so from Newton's third law the air exerts a force on the wings and airplane that is up and slightly backward (Figure 1). The upward force is the lift force that keeps the airplane aloft, and the backward force is called induced drag. At flying speeds, induced drag is inversely proportional to ², so that the total air resistance force can be expressed by Fair = av² + B/v². where a and ß are positive constants that depend on the shape and size of the airplane and the density of the air. To simulate a Cessna 150, a small single-engine airplane, use a = 0.320 N -s²/m² and 3 = 3.59x105 Nm²/s². In steady flight, the engine must provide a forward force that exactly balances the air resistance force. Figure Induced drag Lift Force of air on wings 1 of 1 Part A Calculate the speed at which this airplane will have the maximum range (that is, travel the greatest distance) for a given quantity of fuel. Express your answer in meters per second. VE ΑΣΦΑ V= Submit Part B V= Submit Request Answer Calculate the speed for which the airplane will have the maximum endurance (that is, will remain in the air the longest time). Express your answer in meters per second. ][| ΑΣΦ Provide Feedback ? Request Answer m/s ? m/s
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