(10%) Problem 6: If a inside of the curve (a real problem on icy mountain roads)
ID: 1779568 • Letter: #
Question
(10%) Problem 6: If a inside of the curve (a real problem on icy mountain roads). car takes a banked curve at less than a given speed, friction is needed to keep it from sliding toward the rt (a) Calculate the minimum speed, in meters per second, required to take a 96 m radius curve banked at 19° so that y slide inwards, assuming there is no friction. Grade Surn Potential cosO cotan0asin0 acos0 atanO acotansinhO Submission Attempts ren (5% per atto detailed vie 4 5 6 coshO tanhO cotanhO+ ODegrees Radians VO 10% Submit Hint I give up Hints: 5% deduction per hint. Hints remaining:- Feedback: 29 deduction per feedback. - = 50% Part (b) what is the minimum coefficient of friction needed for a frightened driver to take the same curve at 16 km/h? All consent 2017 Espen TA LCExplanation / Answer
banked curve data :
r = 96 m
= 19°
a equilibrium in ideal conditions requires that centripetal force Fc = m*ac = m*V2/r must equate inner sliding force Fi = m*g*tan....so :
m*V2/r = m*g*tan
V2= r g tan
V = 96 * 9.81 * tan (19) = 17.99 m/sec = 18m/s
if real speed Vr differs from the ideal speed V, then aequilibrium is maintaines by tires transversal friction k such that :
m*Vr2/r±m*g*k = m*g*tan
in case Vr<V , then m*g*k is a positive quantity and must sum up to centripetal force and vice-versa for Vr>V
m cross
k = (g*tan-Vr2/r)/g = (9.8* tan (190)- ( 4.44m/s)2/(96 ) / 9.8 = 0.3232
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