Question

An object resting on an incline without slipping requires friction equal to the component of its weight parallel to the incline. The maximum angle for which the object won't slide down is given by θ=tan−1μs. Which of the following statements supports this conclusion?

a) The coefficient of static friction is inversely proportional to the weight of the object.
b) The tangent of the angle of inclination equals the coefficient of static friction.
c) The maximum angle is directly proportional to the coefficient of static friction.
d) The sine of the angle of inclination equals the coefficient of static friction.

Answer 1

The statement that the tangent of the angle of inclination equals the coefficient of static friction supports the conclusion about the maximum angle for which an object won't slide down an incline.

Step-by-step explanation:

The statement that supports the conclusion that the maximum angle of an incline (θ) above the horizontal for which an object will not slide down is given by θ = tan∑μs is: b) The tangent of the angle of inclination equals the coefficient of static friction. This is because static friction (fs) must balance the component of the gravitational force parallel to the incline (mg sin θ) to prevent the object from sliding. At the maximum angle before slipping occurs, the static friction reaches its maximum value (μsN, where N is the normal force), and since the normal force equals mg cos θ, we get μs mg cos θ = mg sin θ. Therefore, μs = tan θ when the object is on the verge of slipping.