Final answer:
The normal force on a 1100 kg car driving over a circular hill at 30 m/s with a radius of 430 m is found by calculating the centripetal force and subtracting the car's weight from it, due to circular motion dynamics at the top of the hill.
Step-by-step explanation:
To calculate the normal force on a 1100 kg car driving over a circular hill at 30 m/s with a radius of 430 m, we use the concept of centripetal force and the normal force in the context of circular motion.
Firstly, we need to find the centripetal force required to keep the car moving in a circular path. The formula for centripetal force (Fc) is Fc = mv²/r, where m is the mass, v is the velocity, and r is the radius of the circular path. Plugging in our values, we get Fc = (1100 kg)(30 m/s)² / (430 m).
To find the normal force, we consider that at the top of the hill, the normal force (N) and the gravitational force (mg) contribute to the centripetal force. The equation is N + mg = mv²/r. We rearrange to solve for N: N = mv²/r - mg. Using g = 9.8 m/s², we solve for N.
After calculating using the given values, we find that the normal force on the car is less than the gravitational force due to the centripetal acceleration at the top of the hill.