a curve along the highway is to be banked for traffic expected to move at 80km/hr. find the angle of banking if the radius of the curve is 100 meters
80 km/hr * 1 hr/3600s * 1000 m/km
= 22.2 m/s
tan T = v^2/r / g = v^2/gr
tan T = 22.2^2/(981)
tan T = .502
T = 26 deg 39 min
To find the angle of banking for a curved highway, you need to consider the speed of the traffic and the radius of the curve.
The formula to calculate the angle of banking is:
θ = atan(v^2 / (g * r))
Where:
θ is the angle of banking
v is the velocity/speed of the traffic
g is the acceleration due to gravity (approximately 9.8 m/s^2)
r is the radius of the curve
First, convert the speed from km/hr to m/s. Since 1 km = 1000 m, and 1 hour = 3600 seconds:
Speed in m/s = (80 km/hr) * (1000 m / 1 km) * (1 hr / 3600 sec)
Next, substitute the values into the formula:
θ = atan((80 m/s)^2 / (9.8 m/s^2 * 100 m))
Calculating the numerator first:
Numerator = (80 m/s)^2 = 6400 m^2/s^2
Now calculate the denominator:
Denominator = 9.8 m/s^2 * 100 m = 980 m^3/s^2
Finally, substitute the numerator and denominator values into the formula:
θ = atan(6400 m^2/s^2 / 980 m^3/s^2)
Using a calculator, calculate the arctangent (atan) of the ratio:
θ ≈ atan(6.53)
The answer will be in radians. To convert it to degrees, multiply by 180/π:
θ ≈ 0.109 radians = 0.109 * (180/π) degrees
The angle of banking for the curve along the highway is approximately 6.25 degrees.