Final answer:
To find the angle that causes a 25 kg block to slide on an incline with a coefficient of static friction of 0.6, use the maximum static friction formula and gravitational force components, resulting in the angle being tan^{-1}(0.6) or about 30.96 degrees.
Step-by-step explanation:
The angle that causes the block to slide on the incline given the coefficient of static friction of 0.6 can be found using the formula for static friction and the components of the gravitational force along the incline. When the block begins to slide, the static friction is at its maximum value, which is f_s = μ_s ⋅ N, where μ_s is the static friction coefficient and N is the normal force.
In this case, the gravitational force component parallel to the incline is F = mg ⋅ sin(θ), and this must be equal to the maximum static friction force for the block to begin sliding, which gives us mg ⋅ sin(θ) = μ_s ⋅ mg ⋅ cos(θ). From this, we can solve for the angle θ to get θ = tan^{-1}(μ_s). Substituting the given coefficient, θ = tan^{-1}(0.6), we find the angle at which the block will begin to slide down the incline.
Therefore, the angle that causes the block to slide is tan^{-1}(0.6), which we can calculate to be approximately 30.96 degrees.