A 1400 kg car rounds a curve of radius 66 m banked at an angle of 12°. What is the magnitude of the friction force required for the car to travel at 80 km/h?
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To find the magnitude of the friction force required for the car to travel at 80 km/h, we need to consider the forces acting on the car as it rounds the curve.
First, let's find the speed of the car in meters per second (m/s). We can convert the given speed of 80 km/h to m/s by multiplying it by (1000 m / 1 km) and then dividing it by (3600 s / 1 h):
80 km/h * (1000 m / 1 km * 1 h / 3600 s) = 22.22 m/s (rounded to two decimal places)
Next, we need to determine the force of static friction acting on the car. For a banked curve, the force of static friction is responsible for providing the centripetal force required to keep the car moving in a circular path.
The centripetal force (Fc) can be calculated using the formula:
Fc = m * v^2 / r
where m is the mass of the car, v is the speed of the car, and r is the radius of the curve.
Plugging in the values, we have:
Fc = 1400 kg * (22.22 m/s)^2 / 66 m = 10634.92 N (rounded to two decimal places)
Since the friction force (Ff) is equal to the centripetal force (Fc), we have:
Ff = 10634.92 N (rounded to two decimal places)
Therefore, the magnitude of the friction force required for the car to travel at 80 km/h is approximately 10634.92 N.