Final answer:
The minimum speed required to take a 104 m radius curve banked at 13° without sliding inwards is approximately 20.83 m/s.
Step-by-step explanation:
To calculate the minimum speed required to take a banked curve without sliding inwards, we can use the equations for the horizontal and vertical forces acting on the car. In this case, since there is no friction, the only vertical force is the component of the car's weight acting perpendicular to the incline, which is equal to the normal force. The horizontal force is the centripetal force required to keep the car moving in a circle, which is equal to the mass times the radial acceleration. By equating these forces and solving for velocity, we can calculate the minimum speed.
Using the given information, we can plug in the values into the equations. The sine of the banking angle, 13°, can be used to find the normal force, which is equal to the gravitational force. We can then rearrange the equation to solve for the minimum speed, v_min.
v_min = sqrt(g * r * tan(theta))
where g is the acceleration due to gravity, r is the radius of the curve, and theta is the banking angle.
Plugging in the values, we get:
v_min = sqrt(9.8 * 104 * tan(13°))
v_min ≈ 20.83 m/s