Determine the minimum angle at which a roadbed should be banked so that a car traveling at 20 m/s can safely negotiate the curve if the radius of the curve is 200m.
* Data:
v=20 m/s
r=200m
*Formula
TAN(theta)=v^2/rg
*Solution
TAN(theta)=(20 m/s)^2/(200m)(9.8 m/s^2)
TAN(theta)=(400 m^2/s^2)/(1960 m^2/s^2)
TAN(theta)=.204 Degrees
Thank You For Your Time! JL
To determine the minimum angle at which a roadbed should be banked, we can use the formula TAN(theta) = v^2 / (r * g), where v is the velocity of the car, r is the radius of the curve, and g is the acceleration due to gravity.
In this case:
v = 20 m/s (given)
r = 200 m (given)
g = 9.8 m/s^2 (acceleration due to gravity)
Substituting these values into the formula, we have:
TAN(theta) = (20 m/s)^2 / (200 m * 9.8 m/s^2)
TAN(theta) = (400 m^2/s^2) / (1960 m^2/s^2)
TAN(theta) = 0.204
To find the value of theta, we need to find the inverse tangent (TAN^-1) of 0.204. This can be done using a scientific calculator or by looking up the value in a trigonometric table. The inverse tangent of 0.204 is approximately 11.67 degrees.
Therefore, the minimum angle at which the roadbed should be banked for a car traveling at 20 m/s and negotiating a curve with a radius of 200 m is approximately 11.67 degrees.
Please note that this calculation assumes a constant velocity throughout the curve and does not account for other factors like friction, road conditions, or driver behavior. It is a simplified calculation for determining the minimum angle of banking.