Final answer:
To find the minimum coefficient of friction needed for the car to negotiate the curve without slipping, we calculate the centripetal force exerted on the car and divide it by the normal force. The minimum coefficient of friction is approximately 0.16.
Step-by-step explanation:
To determine the minimum coefficient of friction needed for the car to negotiate the curve without slipping, we need to calculate the centripetal force exerted on the car and then use it to find the minimum static coefficient of friction.
First, we calculate the centripetal force using the formula Fc = mv²/r, where m is the mass of the car, v is the velocity, and r is the radius of the curve. The centripetal force is given by Fc = (1800 kg)(40 m/s)²/(100 m) = 288,000 N.
Next, we calculate the normal force N using the formula N = mg, where g is the acceleration due to gravity. The normal force is equal to the weight of the car, which is given by N = (1800 kg)(9.8 m/s²) = 17,640 N.
Finally, we find the minimum static coefficient of friction using the formula µs = Ff/N, where Ff is the maximum force of static friction. The maximum force of static friction is equal to the centripetal force, so we have µs = 288,000 N/17,640 N ≈ 16.33.
Therefore, the minimum coefficient of friction needed for the car to negotiate the curve without slipping is approximately 0.16.