Part A A curve with an average radius of 80 meters is banked for a design speed

Question

Part A

A curve with an average radius of 80 meters is banked for a design speed of 85 kilometers per hour. Determine the angle at which the curve has been banked (by design).

Note: g 9.81 m/s2

Part B

A curve with an average radius of 60 meters has been banked at an angle of 30º. Determine the exact speed at which a vehicle can safely negotiate the curve if there is no friction.

Part C

A curve with an average radius of 75 meters has been banked at an angle of 32.5º. If the coefficient of friction between the surface of the banked curve (wet pavement) and the tires of the vehicle is s = 0.30, determine the maximum speed at which the vehicle can safely negotiate the curve.

Part D

A curve with an average radius of 75 meters has been banked at an angle of 32.5º. If the coefficient of friction between the surface of the banked curve (wet pavement) and the tires of the vehicle is s = 0.30, determine the minimum speed at which the vehicle can safely negotiate the curve.

Explanation / Answer

Part A)

Given that R = 80 m

speed is V = 85 kmpH = 85*1000/3600 = 23.6 m/sec

tan(theta) = v^2/(R*g) = 23.6^2/(80*9.81) = 0.71

theta = tan^(-1)(0.71) = 35.4 deg

Part B)

tan(theta) = v^2/(R*g)

tan(30) = v^2/(60*9.81)

v = 18.43 m/sec = 18.43*(3600/1000) = 66.34 kmpH

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