PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
A wooden block of mass 12kg rests on a 30∘ rough incline. A rope exerts a force F∥ directed up the incline. The smallest value of the applied force that just initiates upward motion is measured to be 70N. Ignore any air resistance and assume the coefficient of kinetic friction is equal to the coefficient of static friction at the threshold of motion.
(a) Draw and label a free-body diagram for the block, showing all forces acting on it.
(b) Resolve the gravitational force on the block into components parallel and perpendicular to the surface of the incline, expressing each component symbolically in terms of m, g, and the incline angle θ.
(c) Derive an expression for the coefficient of static friction μs in terms of known quantities by applying equilibrium conditions at the threshold of upward motion.
(d) Substitute the given numerical values to determine μs for the wood–incline interface.