Final answer:
Static friction is responsible for keeping an object stationary on an incline up to a certain angle, which is determined by the static coefficient of friction and can be calculated using the arctan of the static friction coefficient.
Step-by-step explanation:
The maximum force that static friction can exert to prevent an object on an incline from sliding is directly related to the static coefficient of friction (μs), the angle of the incline (θ), and the normal force. This force is crucial in determining whether an object will remain stationary or begin to slide down an inclined surface. The maximum angle (θ) for which an object will not slide down can be expressed as θ = tan⁻¹ (μs), assuming that static friction has reached its maximum value and acceleration (a) is zero.
For example, if a crate has a mass of 100 kg and is resting on a horizontal surface, the normal force would be equal to its weight (N = mg = (100 kg)(9.80 m/s²) = 980 N). If the coefficient of static friction (μs) is 0.45, the maximum force of static friction (fs(max)) that must be overcome to start moving the crate would be fs(max) = μsN = (0.45)(980 N) = 440 N. Once the crate is in motion, kinetic friction takes effect and it requires less force to maintain movement.