Question

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)

Answer 1

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.