Final answer:
To calculate the minimum coefficient of friction for a car to negotiate an unbanked curve, we use the equation: µ = v^2/(rg), where µ is the coefficient of friction, v is the velocity of the car, r is the radius of the curve, and g is the acceleration due to gravity.
Step-by-step explanation:
To calculate the minimum coefficient of friction needed for a car to negotiate an unbanked curve, we need to consider the centripetal force acting on the car.
The centripetal force is given by the equation: Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the car, v is the velocity, and r is the radius of the curve.
In this case, the car has a mass of m, a velocity of v, and is traveling along a curve with a radius of r. The minimum coefficient of friction needed for the car to negotiate the curve is equal to µ = Ff/Fn, where Ff is the frictional force and Fn is the normal force.
To find the normal force, we can use the equation: Fn = mg, where m is the mass of the car and g is the acceleration due to gravity.
Substituting the equations for centripetal force and normal force into the equation for the coefficient of friction, we get:
µ = (m(v^2)/r)/(mg) = v^2/(rg).
Therefore, the minimum coefficient of friction needed for the car to negotiate the unbanked curve is given by the equation: µ = v^2/(rg).