Final answer:
Using physics equations related to centripetal force and the normal force on a banked curve, the minimum speed can be calculated by solving the formula v = √(gr tan(θ)) for v, inputting the given values of gravity, radius, and banking angle.
Step-by-step explanation:
To calculate the minimum speed required to take a 92 m radius curve banked at 17° without sliding inwards, and assuming there is no friction, we can use the following physics principles. The centripetal force required to make the car follow the curved path is provided by the horizontal component of the normal force. Since there is no friction, and we are ignoring gravitational forces pulling the car towards the center, the entire centripetal force is due to the normal force's horizontal component.
Using the centripetal force equation Fc = mv2/r and the fact that the centripetal force is also equal to N sin(θ), where N is the normal force and θ is the banking angle, we set up the equation mv2/r = N sin(θ). Since the only force acting on the car vertically is its weight, N must also be equal to mg/cos(θ).
By combining these equations and solving for v, we get the following formula: v = √(gr tan(θ)). Substituting the given values of g = 9.81 m/s2, r = 92 m, and θ = 17°, we can calculate the minimum speed.
Steps to calculate the minimum speed:
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Performing the calculation gives us the minimum speed in meters per second.