Final answer:
The weight of the car is calculated by rearranging the centripetal force equation and substituting the given values. The car's weight is found to be 15003 N.
Step-by-step explanation:
Calculating the Car's Weight from Centripetal Force
To find the weight of the car, we use the relationship between centripetal force, mass (m), velocity (v), and radius (r) of the circle along which the car is traveling. The equation for centripetal force is Fc = mv2/r, where Fc is the centripetal force, m is the mass, v is the velocity, and r is the radius of the circular path. Given that the centripetal force (Fc) is 6120 N, the velocity (v) is 20 m/s, and the radius (r) of the circle is 100 m, we can rearrange the formula to solve for the mass (m): m = Fc × r / v2.
Now, substituting the given values into the equation, we obtain: m = 6120 N × 100 m / (20 m/s)2 = 6120 N × 100 m / 400 m2/s2 = 6120 N × 0.25 s2/m = 1530 kg. The weight of the car is the mass multiplied by the acceleration due to gravity (g = 9.81 m/s2), giving us w = mg. Therefore, the weight of the car is 1530 kg × 9.81 m/s2 = 15003 N.
The normal force (N) on a level road is equivalent to the weight of the car since it opposes the gravitational force, indicating that the car's weight is 15003 N.