What is the centripetal force exerted on an automobile rounding a curve?
Final answer: To calculate the centripetal force exerted on an automobile rounding a curve, use the formula Fc = m * v^2 / r with the mass of 1.96 x 10^3 kg, velocity of 14.0 m/s, and radius of 27.0 m. The calculated centripetal force is 1.42 x 10^4 N.
Calculating Centripetal Force
Centripetal force is the force required to keep an object moving in a circular path. In the case of an automobile rounding a curve, this force ensures that the car maintains its trajectory without veering off the road. The formula to calculate centripetal force is Fc = m * v^2 / r, where m represents the mass of the object, v is the velocity, and r is the radius of the curve.
Given Data
The mass of the automobile is 1.96 x 10^3 kg, the velocity is 14.0 m/s, and the radius of the curve is 27.0 m.
Calculation
Plugging these values into the formula, we get:
Fc = (1.96 x 10^3 kg) * (14.0 m/s)^2 / 27.0 m
Fc = (1.96 x 10^3 kg) * 196 m^2/s^2 / 27.0 m
Fc = 1.4204 x 10^4 N
Therefore, the centripetal force exerted on the automobile rounding the curve is 1.42 x 10^4 N. This force is crucial for maintaining the car's path and preventing it from skidding off the road.