as you are riding in a 1650-kg car, you approach a hairpin curve in the road whose radius is 50m. the roadbed is banked inward at anangle of 10 degrees.

suppose that the road is dry and that the static friction coefficient between the tires and the asphalt road is .6 what is the maximum speed at which you can safely go around the curve.

To determine the maximum speed at which you can safely go around the hairpin curve, we need to consider the two forces acting on the car: the gravitational force and the frictional force.

1. Gravitational Force:
The gravitational force acting on the car can be calculated using the formula: Fg = m * g, where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Fg = 1650 kg * 9.8 m/s^2 = 16170 N

2. Frictional Force:
The frictional force is responsible for providing the necessary centripetal force to keep the car moving in a circular path. In this case, the frictional force is supplied by the static friction between the tires and the road.

The centripetal force can be calculated using the formula: Fc = (m * v^2) / r, where v is the speed of the car and r is the radius of the curve.
Fc = (1650 kg * v^2) / 50 m

The maximum static friction force that can be provided is given by: Fs = μs * N, where μs is the static friction coefficient and N is the normal force acting on the car.

The normal force can be calculated using the formula: N = m * g * cos(θ), where θ is the banking angle of the road.
N = 1650 kg * 9.8 m/s^2 * cos(10°)

Since the frictional force provides the centripetal force, we can equate the two forces:
(1650 kg * v^2) / 50 m = μs * (1650 kg * 9.8 m/s^2 * cos(10°))

Now we can solve for v to find the maximum speed:
v^2 = (μs * 50 m * 9.8 m/s^2 * cos(10°)) / 1650 kg
v = √[(μs * 50 m * 9.8 m/s^2 * cos(10°)) / 1650 kg]

Substituting the given values:
v = √[(0.6 * 50 m * 9.8 m/s^2 * cos(10°)) / 1650 kg]
v ≈ 10.33 m/s

Therefore, the maximum speed at which you can safely go around the curve is approximately 10.33 m/s.