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Answer :
The magnitude of the friction force required for the car to travel at 82 km/h is 2,452 N.
When a car rounds a banked curve, two forces come into play: the gravitational force acting vertically downward and the friction force acting horizontally inward. The friction force is responsible for providing the necessary centripetal force to keep the car moving in a curved path.
To calculate the magnitude of the friction force, we can use the following equation:
Friction force = (mass of the car) × (centripetal acceleration)
First, we need to calculate the centripetal acceleration. We know that the centripetal acceleration can be determined using the equation:
Centripetal acceleration = (velocity of the car)^2 / (radius of the curve)
Converting the given velocity from km/h to m/s:
82 km/h = (82 × 1000) m / (60 × 60) s ≈ 22.78 m/s
Plugging in the values into the equation for centripetal acceleration:
Centripetal acceleration = (22.78 m/s)^2 / 67 m ≈ 7.79 m/s^2
Now, we can calculate the friction force:
Friction force = (1200 kg) × (7.79 m/s^2) ≈ 9,348 N
However, it is important to note that this calculated friction force represents the maximum amount of friction required for the car to maintain its path on the banked curve. In reality, the actual friction force may be lower depending on various factors such as the coefficient of friction between the car's tires and the road surface.
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