Final answer:
The minimum coefficient of friction needed for the car to negotiate the unbanked curve is approximately 0.29.
Step-by-step explanation:
The centripetal force required for a car to negotiate an unbanked curve can be calculated using the equation:
Fc = mv²/r
Where Fc is the centripetal force, m is the mass of the car, v is its velocity, and r is the radius of the curve. Rearranging the equation gives:
r = mv²/Fc
Plugging in the given values:
r = (1400 kg)(12 m/s)²/(Friction force)
Since the friction force is equal to the centripetal force, the equation becomes:
r = (1400 kg)(12 m/s)²/(μmg)
Where μ is the coefficient of friction and g is the acceleration due to gravity.
Given radius = 50m, m = 1400kg, v = 12 m/s, g ≈ 9.8 m/s², plugging in the values and solving for μ:
μ = (1400 kg)(12 m/s)²/[(50m)(9.8 m/s²)(1400 kg)]
μ ≈ 0.29
Therefore, the minimum coefficient of friction needed for the car to negotiate the unbanked curve is approximately 0.29.