# 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

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