Statics #03 | Equilibrium of a Particle: ΣF = 0 for a Crate on a Ramp and a Lamp on Two Cables

Instructor: Dr. Süleyman Burak ÇELİK

Last lesson we drew two free body diagrams; in this lesson we turn them into numbers. One sentence is enough: the forces acting on a body at rest add up to zero. We turn that sentence into two equations and show every step with numbers. In this lesson: - From Newton's first law to sigma F = 0; the closed force polygon intuition - Sigma Fx = 0 and sigma Fy = 0: two equations, at most two unknowns; the particle assumption - The five-step method: diagram, axes, components, two equations, solve and check - Problem A: 50 kg crate on a smooth 30 degree ramp held by a rope parallel to the ramp. W = 490.5 N; parallel component 490.5 times 0.5 = 245.25 N; perpendicular component 490.5 times 0.866 = 424.8 N; T = 245.25 N, N = 424.8 N; Pythagoras check - Problem B: 20 kg lamp on two cables at 30 and 60 degrees to the ceiling. W = 196.2 N; from the x equation T2 = 1.732 T1; from the y equation 2 T1 = 196.2; T1 = 98.1 N, T2 = 169.9 N; the cables are perpendicular, so Pythagoras checks - Four classic traps: the N = W reflex, sine and cosine from the wrong angle, sign errors, and solving two unknowns with one equation Chapters: 0:00 Intro 0:03 Two diagrams, one sentence 0:55 Why the forces add up to zero 2:35 The five-step method 3:43 Problem A: crate on the ramp 6:33 Problem B: lamp on two cables 9:40 Four traps and one habit 11:09 Summary and what comes next Next lesson: the moment of a force; the size of the body enters the picture. Statics (Engineering Mechanics) series, lesson 3.