F.4 Phy circular motion 急2

2014-05-19 4:02 am

5. An aircraft is flying at a constant speed of 500 km/h in a horizontal circle of
radius 4 km .

b)To turn around,the aircraft is banked .State how this produces the centripetal
force necessary for the circular motion.

d) if the mass of the airplane is 2500 kg,what must be the total lift produced by the
wings?

回答 (1)

天同

2014-05-19 4:43 am

✔ 最佳答案

(b) Because the lifting force is always acting perpendicular to the wings, when the aircraft is banked, the lifting force becomes tilted at some angle with the vertical. This provides a horizontal force component, giving the necessary centripetal force for the aircraft to turn around.

(d) Let F be the total lifting force, and a be the angle at which the aircraft is banked.
Hence, we have,
Horizontally, F.sin(a) = mv^2/R
where m is the mass of the aircraft
v is the speed of the aircraft
R is the radius of the turn

Vertically, F.cos(a) = mg where g is the acceleration due to gravity
Dividing, sin(a)/cos(a) = v^2/Rg
i.e. tan(a) = (500/3.6)^2/4000 x 10 (take g = 10 m/s^2)
a = 25.75 degrees

Therefore, F = mg/cos(25.75) N = 27,760 N

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