Statics #01 | Force and Its Components: Vectors, Resultant and Resolving Forces (Worked Example)

Instructor: Dr. Süleyman Burak ÇELİK

A crate is stuck on the ground and two people pull it with two ropes: one with 400 N at 30 degrees above the horizontal, the other with 300 N up and to the left at 60 degrees. Which way does the crate want to go, and how hard is it pulled in total? That is the very first question of statics: taking several forces and reducing them to a single effect. In this lesson we solve it step by step, skipping nothing. In this lesson: - What a force really is: magnitude, direction, point of application; vector versus scalar - How much is 400 N? A feel for magnitude with an apple, a bag and a 40 kg load - The classic trap: why 400 plus 300 is not 700; tip-to-tail addition, the triangle rule and the parallelogram law - The range rule: the resultant always lies between the difference and the sum of the magnitudes - Resolving a force into components: cosine with the adjacent side, sine with the opposite side, and what changes when the angle is measured from the y axis - The sign rule: components pointing left or down are negative - Full worked example: F1x = 346.4 N, F1y = 200 N, F2x = minus 150 N, F2y = 259.8 N, Rx = 196.4 N, Ry = 459.8 N, R approximately 500 N at about 66.9 degrees - Three checks: the range, the direction, and the 3-4-5 triangle that gives exactly 500 N; where the wrong answers 700 and 676 come from Chapters: 0:00 Intro 0:03 Two ropes, one crate: the problem 0:53 What is a force? A vector 2:11 Adding forces: tip to tail 3:30 Resolving a force into components 4:57 Worked example: every step 7:42 Does it make sense? Three checks 8:58 Summary and what comes next Next lesson: the free body diagram, the art of drawing every single force acting on a body without forgetting any. First lesson of the Statics (Engineering Mechanics) series for civil, mechanical and mechatronics engineering students.