Final answer:
The equation for the maximum angle of an incline above the horizontal for which an object will not slide down is θ = tan^-1(μs), where μs is the coefficient of static friction.
Step-by-step explanation:
The equation for the maximum angle of an incline above the horizontal for which an object will not slide down is given by the formula θ = tan-1(μs), where μs is the coefficient of static friction.
To understand this, we need to consider the forces acting on the object. The force of gravity can be broken down into two components: the component parallel to the incline and the component perpendicular to the incline. For the object to not slide down the incline, the frictional force, which is equal to the component of the weight parallel to the incline, must be equal to or greater than the gravitational force trying to pull the object down.
The maximum angle occurs when the maximum static frictional force is just enough to balance the gravitational force. This maximum static frictional force is given by μs times the normal force, where the normal force is the force perpendicular to the incline acting on the object. Therefore, the maximum angle can be found by setting the maximum static frictional force equal to the gravitational force and solving for the angle.