Final answer:
The angle at which a mass starts sliding off the surface of a sphere occurs when the gravitational force component exceeds the maximum static friction. Using the equation based on the balance of forces, and a coefficient of static friction of 0.55, we can calculate this angle using inverse tan function: θ = tan⁻¹(0.55).
Step-by-step explanation:
The question concerns the condition under which a small mass will begin to slide off the surface of a sphere, given a certain coefficient of static friction. This scenario is a classic problem in physics, specifically, in the study of mechanics and friction.
To determine the angle at which the mass starts sliding, one would typically resolve forces parallel and perpendicular to the surface of the sphere at the point of contact and employ the concept of static friction. For a sphere, a mass will start sliding off when the component of gravitational force along the surface of the sphere exceeds the maximum static frictional force. The condition for the beginning of the slide is when the tangential component of weight equals the static frictional force, i.e., mg sin(θ) = μs mg cos(θ), where m is the mass of the object, θ is the angle of inclination, g is the acceleration due to gravity, and μs is the coefficient of static friction. Simplifying this equation gives tan(θ) = μs, and invoking trigonometric functions to find θ gives θ = tan−1(μs). For a coefficient of static friction of 0.55, the angle θ at which the mass starts sliding is θ = tan−1(0.55).