A block of mass rests on a smooth plane inclined at to the horizontal
PHYSICS · Subjective · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A block of mass 10kg rests on a smooth plane inclined at 30∘ to the horizontal. A horizontal force P is applied to the block (acting up the plane side of the block) in such a way that the block remains at rest.
Take g=9.8ms−2.
(a) Draw a free-body diagram showing all forces acting on the block and label their directions clearly.
(b) Resolve each force into components parallel and perpendicular to the plane and write the two independent equilibrium equations.
(c) Calculate the magnitude of the horizontal force P required to keep the block in equilibrium.
(d) Determine the normal reaction exerted by the plane on the block.
(e) If the plane were rough with a coefficient of static friction μs=0.2, discuss whether the same horizontal force P would still keep the block at rest. Support your answer with suitable numerical reasoning.