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A curve of radius 72m is banked for a design speed of 125km/h . If the coefficient of static friction is 0.34 (wet pavement), at what range of speeds can a car safely handle the curve? Express your answers using two significant figures. Enter your answers numerically separated by a comma.Explanation / Answer
for perfect banking
mg*sin(theta)=mv^2*cos(theta)/R
==> tan(theta) = v^2/Rg=(125/3.6)^2/72*9.8=1.71
==> theta = 59.66 degrees
now with friction
there are two cases
Case 1 :: friction acts in downward direction
mg*sin(theta)+mu*mg*cos(theta)=mv^2*cos(theta)/R
==> [sin(59.66 degrees) +0.34*cos(59.66 degrees)]*72*9.8= v^2*cos(59.66 degrees)
==> 730.145= v^2*cos(59.66 degrees)
==> v=38.019 m/s=136.87 Km/h
Case 2 :: friction acts in upward direction
mg*sin(theta)-mu*mg*cos(theta)=mv^2*cos(theta)/R
==> [sin(59.66 degrees) -0.34*cos(59.66 degrees)]*72*9.8= v^2*cos(59.66 degrees)
==> 487.78= v^2*cos(59.66 degrees)
==> v=31.07 m/s=111.87 Km/h
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