Answer :
Final answer:
The car's circular motion on the banked curve requires a certain amount of centripetal force. Given the speed of the car, the mass, and radius of the curve, the bank angle isn't providing enough gravitational force towards the center of the curve. Therefore, friction must be present and exerted towards the center of the curve to maintain this motion.
Explanation:
The subject of this question is Physics, specifically the physics of circular motion and friction. The car is rounding a banked curve, which requires a certain amount of centripetal force to keep it moving in a circular path. The centripetal force is provided by two components, the normal force and the force due to gravity.
When the angle of the bank and the speed of the car are perfectly matched, no frictional force is required because the component of the gravitational force in the direction of the center of the curve balances the required centripetal force.
In this case, the speed of the car (95 km/h = 26.39 m/s), the mass of the car (1200 kg), and the radius of the curve (67 m) would require a certain frictional force, because the bank angle (12 degrees) is not steep enough to provide the required centripetal force by gravity alone. The required centripetal force can be calculated by the equation F = mv²/r, where m is mass, v is velocity, and r is radius. The gravity component adds to the normal force to give a net external force that is horizontal toward the center of curvature.
Calculating for the required centripetal force results in a frictional force necessary to maintain the car's circular motion. Thus, friction would indeed be necessary to keep the car on the road, and it will be exerted towards the center of the curve.
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