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A 1400 kg car rounds a curve with a radius of 72 m, banked at an angle of 14 degrees. What is the magnitude of the friction force required for the car to travel at 84 km/h?

Answer :

The magnitude of the friction force required for the car to travel at 84 km/h is 105623.15 N.

To find the magnitude of the friction force required for the car to travel at 84 km/h, we can use the concept of centripetal force.

First, we need to calculate the speed of the car in meters per second. We convert 84 km/h to m/s by dividing it by 3.6.

Therefore, the car's speed is 23.33 m/s.

Next, we can find the net force acting on the car using the equation F_net = m * v^2 / r, where F_net is the net force, m

is the mass of the car, v is the velocity, and r is the radius of the curve.

Plugging in the values, we get F_net = (1400 kg) * (23.33 m/s)^2 / (72 m).

Calculating this, we find F_net = 105623.15 N.

Since the car is traveling in a curved path, there is a vertical component of the normal force that balances the weight of the car. The horizontal component of the normal force provides the necessary friction force for the car to travel in the curve.

Therefore, the magnitude of the friction force required for the car to travel at 84 km/h is 105623.15 N.

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