Final answer:
The angle of static friction, or the angle of repose, is the maximum angle a plane can be tilted before an object begins to slide. By setting the maximum static friction force equal to the object's weight component parallel to the incline, the angle can be calculated as the inverse tangent of the coefficient of static friction. With a coefficient of 0.23, the angle is found to be approximately 12.99 degrees.
Step-by-step explanation:
To find the angle of static friction, also known as the angle of repose, we relate the maximum static friction force to the weight component of the block parallel to the plane.
The force of static friction (Ffriction) is given by Ffriction = μs × N, where μs is the coefficient of static friction and N is the normal force.
At the point of impending motion, Ffriction equals the weight component (Wparallel) parallel to the slope,
Wparallel = W × sin(θ), with W being the weight of the block and θ the angle of incline.
Because N = W × cos(θ) and Ffriction must balance Wparallel, setting Ffriction equal to Wparallel gives us
μs × (W × cos(θ)) = W × sin(θ).
Simplifying and solving for θ, we get θ = tan-1(μs).
Using the given coefficient of static friction, 0.23, the angle of static friction is θ = tan-1(0.23).
Calculating this gives an angle of approximately 12.99 degrees.