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Curve Track

radius of curvature for a racecar track?

There is a banked curve track and a car goes 120km/h around it. It doesn't depend on the force of friction to keep it on the track. If the turn is 25 degress to the horizontal what is its radius of curvature?

Solution :

tangent @ = (v^2)/gR

where :
@ = angle of banking = 25 degrees
v = velocity
g = gravitational force = 9.81m/sec^2
R = radius of curve

R = (v^2)/(g x tangent @)
R = ((120km x 1000m/km)/(hour x 1hr/3,600 sec))^2 / (9.81m/sec^2 x tangent 25 degrees)
R = (1,111.111/4.574)
R = 242.894 meters say 242.90 meters (Answer)

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