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# Circular motion

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A plane heading due North makes a level turn with a speed of 100 m/s. The angle of the bank is 15 degrees. Determine:

(a) Radius of the circular path
(b) Cetripetal acceleration
(c) Lift force
(d) Direction of velocity after 30 seconds (Weight of the plane is 19600 Newtons)

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Let the lift be L which acts perpendicular to the plane's wings

mg= 19600 N
m= 1997.96 kg as g=9.81 m/s
v= 100 m/s

L Cos 15 =mg=weight= 19600 N ----(1)
L Sin 15=centripetal force=m v ^2/r ----(2)

Dividing (2) by (1)

tan 15=(m v ^2/r)/mg =v^2/gr

or r=v^2/g Tan 15= 3804.33 m

Centripetal acceleration=v^2/r= 2.63 m/s^2

Lift force=L=mg/Cos15= 20291.41 N

Angular velocity=v/r= 0.026285837 rad/s= 1.5 degrees/s
In 30 seconds angle covered=1.5*30= 45 degrees

Direction of velocity =45 degrees East from due North

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!