We can start by finding the acceleration of the body using the centripetal acceleration formula:
a = v^2 / r
Where:
a = acceleration
v = velocity = 120 m/s
r = radius = 100 m
Substituting the given values:
a = (120^2) / 100
a = 14400 / 100
a = 144 m/s^2
Now, we can determine the banking angle (θ) using the equation:
tan(θ) = a / g
Where:
θ = banking angle
a = acceleration = 144 m/s^2
g = acceleration due to gravity = 9.8 m/s^2
Substituting the given values:
tan(θ) = 144 / 9.8
Taking the inverse tangent on both sides:
θ = tan^(-1)(144 / 9.8)
θ ≈ 83.6 degrees
Therefore, the banking angle of the track is approximately 83.6 degrees.
If a body is moving in a circular track of radius 100m with a velocity of 120m/s determine the banking angle of the track (g=9•8m/s)
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