Statics Test 1 Review By Caleb

Chapter 2 The stuff you should know: Laws of Motion Finding resultant forces In 2D Non-orthogonal axes Law of Sines, Law of Cosines, Parallelogram law, Head to Tail Addition Orthogonal Add Cartesian Vectors(especially if more than 3 forces) In 3D Sum Cartesian Vectors to get resultant vector Use position vectors to get the unit vectors To get coordinate direction angles, take arccos of the components of unit vector Use Dot product to get component of force along axis or other components

Ch 2 Practice Problem: Dot Product Find the component of force F acting along BC

Ch 2 Practice Problem: Dot Product Process: Find uBC and uF Find Cartesian coordinates of F Use dot product of uBC and F to get magnitude of the component

Chapter 3 Systems in Equilibrium A lot of the basics from 3 remain the same, but there are some differences: All problems are in equilibrium, so the total sum of the forces is 0 By extension, the sum of forces in the x, y, and z directions is also 0 Instead of solving for a resultant force, we solve for one of the forces in the system New components of statics problems are introduced Springs: F = ks where k is spring constant and s is distance deformed Pullies: Tension on the rope on both sides of the pulley is the same

Ch 3 Practice Problem 3D Vectors If the bucket has a weight of 20lb and FDA is 10lb, what is the tension in FDB and FDC?

Ch 3 Practice Problem 3D Vectors Process: Find the unit vectors of FDA and FDC Find the Cartesian forms of each of the vectors Sum the forces in the x, y, and z directions to get equations

Chapter 4 Moments Some of you may not have done moments yet, so lets do the basics: A moment is a force that can cause a body to rotate The magnitude of the produced moment can represented by the equation M = Fd F is the force acting perpendicularly to the line of action through the point the moment is being taken about d is the distance to the perpendicular force from the point the moment is being taken about http://www.learneasy.info/MDME/MEMmods/MEM30005A/moments/Moments.html

Ch 4 Examples M = F * d So what is the moment about O?

Ch 4 Examples M = 100N * (2m) = 200 N*m CCW Force is a perpendicular distance 2m away from point O

Ch 4 Examples M = F * d

Ch 4 Examples M = F * d M = -500N 3 5 * 2m = -600 N*m CW Since the 500 N is not perpendicular to the line of action through O, we must get the portion of the force that is perpendicular. Forces that act through the line of action do not cause a moment.

Ch 4 Examples M = F * d

Ch 4 Examples M = F * d M = 500N 4 5 * 1m – 500N 3 5 * 2m = (400 – 600)N*m = -200 N*m CW Both components of the force are perpendicular to the line of action, but they work in opposite directions. The typical conventions make a moment moving Clockwise(CW) negative and Counter Clockwise(CCW) positive. Always label your answer.