Question

A car can negotiate an unbanked curve safely at a certainmaximum speed when the coefficient of static friction between thetires and the ground is 0.794. At what angle should the same curvebe banked for the car to negotiate the curve safely at the samemaximum speed without relying on friction?

Answer 1

To determine the angle at which the curve should be banked for a car to negotiate it safely without relying on friction, we can use the formula tan(θ) = v^2 / (g * r). Given the coefficient of static friction, we can calculate the maximum speed at which the car can negotiate the unbanked curve and use it to solve for the angle θ.

Step-by-step explanation:

A car can negotiate a curve safely without relying on friction when the curve is banked at a certain angle. To determine the angle at which the curve should be banked, we can use the formula:

tan(θ) = v^2 / (g * r)

Where θ is the angle of the bank, v is the velocity of the car, g is the acceleration due to gravity, and r is the radius of the curve.

Given that the coefficient of static friction is 0.794, we can calculate the maximum speed at which the car can negotiate the unbanked curve using the equation:

μ = tan(θ)

By substituting the value of the coefficient of static friction into the equation, we can solve for θ.