Chapter 5

5.1 Vectors  Shows both direction and magnitude  Can act in multiple directions at given time Must be drawn at appropriate angles to evaluate system Tip to Tail addition to get resultant Pythagorean Theorem, Law of Sines, Law of Cosines

Ex Prob 1, pg 121  Find the magnitude of the sum of a 15 km displacement and a 25 km displacement when the angle between them is 90 degrees and when the angle between them is 135 degrees.

Vector Components  All vectors can be placed on a coordinate grid  Vectors can be broken into pieces that are perpendicular to each other (if not already) x-components and y-components Process called vector resolution Original vector will be resultant of components

Vector Math  A x = A cos   A y = A sin   Sometimes know vectors, but no angle Fig 5-5, pg 123  Angle of resultant vector  = tan -1 (R y /R x ) A = Ax + Ay

5.2 Friction  Force that opposes the direction of motion  Two types Kinetic ○ Force exerted when one surface rubs against another surface Static ○ Force exerted on one surface by another when there is no motion ○ Limit to size

Friction  Depends on material and normal force NOT surface area or speed  Graph of kinetic frictional force versus normal force Slope is coefficient of kinetic friction,  k F f,k =  k F N  Static friction is similar Coefficient of static friction,  s F f,s ≤  s F N

5.3 Force and Motion in 2D  System in equilibrium when F net = 0 Motionless or constant velocity  Equilibrant is vector that puts system in equilibrium  Challenge problem, pg 132

Inclined Planes  Align coordinate system so x-axis is on ramp surface  Find components so all vectors align along x- and y-axes  Normal force will not be equal to weight

labs  Friction lab, pg  Inclined plane lab, pg  Revise friction lab to make it only friction – different surfaces  Revise inclined plane lab to make it multiple angles for same surface