Circular motion
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)
https://brainmass.com/physics/circular-motion/radius-cetripetal-acceleration-lift-force-velocity-direction-11013
SOLUTION This solution is FREE courtesy of BrainMass!
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)
r=Radius of the circular path
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
© BrainMass Inc. brainmass.com December 24, 2021, 4:50 pm ad1c9bdddf>https://brainmass.com/physics/circular-motion/radius-cetripetal-acceleration-lift-force-velocity-direction-11013