How Fast Can a Car Go Around a 65m Curve with a Friction Coefficient of 0.54?

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The maximum speed a car can navigate a 65m curve with a friction coefficient of 0.54 is determined by the balance of forces acting on the vehicle. The centripetal acceleration required for circular motion must equal the frictional force available. By summing the forces in the radial direction, one can calculate the maximum speed using the formula for centripetal force. This involves applying the equation that relates friction, mass, and acceleration. Understanding these principles is essential for determining safe driving speeds on curves.
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What is the maximum speed that a car can go around a curve with a radius of 65m if the coefficient of friction is 0.54?
 
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If you have circular motion you must have a centripetal acceleration acting toward the center of the circle. So sum the forces in the radial direction and set that equal to the centripetal force.
 
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