CALC 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 ( Fig. P6.94 ). 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 υ 2 , so the total air resistance force can be expressed by F sir = α υ 2 + β / υ 2 . where α and β are positive constants that depend on the shape and size of the airplane and the density of the air. For a Cessna 150, a small single-engine airplane, α = 0.30 N • s 2 /m 2 and β = 3.5 × 10 5 N • m 2 /s 2 . In steady flight, the engine must provide a forward force that exactly balances the air resistance force, (a) Calculate the speed (in km/h) at which this airplane will have the maximum range (that is. travel the greatest distance) for a given quantity of fuel, (b) Calculate the speed (in km/h) for which the airplane will have the maximum endurance (that is, remain in the air the longest time).
CALC 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 ( Fig. P6.94 ). 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 υ 2 , so the total air resistance force can be expressed by F sir = α υ 2 + β / υ 2 . where α and β are positive constants that depend on the shape and size of the airplane and the density of the air. For a Cessna 150, a small single-engine airplane, α = 0.30 N • s 2 /m 2 and β = 3.5 × 10 5 N • m 2 /s 2 . In steady flight, the engine must provide a forward force that exactly balances the air resistance force, (a) Calculate the speed (in km/h) at which this airplane will have the maximum range (that is. travel the greatest distance) for a given quantity of fuel, (b) Calculate the speed (in km/h) for which the airplane will have the maximum endurance (that is, remain in the air the longest time).
CALC 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 (Fig. P6.94). 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 υ2, so the total air resistance force can be expressed by Fsir = α υ2 + β/υ2. where α and β are positive constants that depend on the shape and size of the airplane and the density of the air. For a Cessna 150, a small single-engine airplane, α = 0.30 N • s2/m2 and β = 3.5 × 105 N • m2/s2. In steady flight, the engine must provide a forward force that exactly balances the air resistance force, (a) Calculate the speed (in km/h) at which this airplane will have the maximum range (that is. travel the greatest distance) for a given quantity of fuel, (b) Calculate the speed (in km/h) for which the airplane will have the maximum endurance (that is, remain in the air the longest time).
A 325-g model boat facing east floats on a pond. The wind in its sail provides a force of 1.55 N that points 25° north of east. The
force on its keel is 0.655 N pointing south. The drag force of the water on the boat is 0.750 N toward the west.
If the boat starts from rest and heads east, what is its final speed vf after it travels for a distance of 3.85 m?
Uf =
m/s
Q2: Jane, who weighs 500 N, must cross a river full of hungry crocodiles to save Tarzan, who weighs 700 N, from danger. She jumps (from rest) off a cliff hanging from the end of an 18 m long vine, Fig.length, Fig. 1(b). From the top of the cliff to the lowest point of the trajectory she descends 3.0 m. The vine will breakif the force exerted on it exceeds 650 N.(a) Show that she will not be able to reach Tarzan?(b) And determine the angle of rupture θ, with respect to vertical.(c) Using a rope strong enough to hold them both, Jane rescues Tarzan. What will be the speed of thetwo when Jane "grabs" him (assume Jane is strong enough to hold him)?(d) Is the energy conserved? If yes, justify, if no, calculate∆K/Ki and explain what happened to the energy.
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. 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 v
2
, so that the total air
resistance force can be expressed by
Fair = av2 + b/v2
where a and b are positive constants that depend on the shape and size of
the airplane and the density of the air.
For a Cessna 150, a small single-engine airplane, a = 0.30 N.s2
/m2 and
b = 3.5×105 N.m2
/s
2
. In steady flight, the engine must provide a forward force
that exactly balances the air resistance force.
1. Calculate the speed (in km/h) at which this airplane will have the…
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