Transcript Forces in two dimensions

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
Ax = A cos q
 Ay = A sin q


A = Ax + Ay
Sometimes know vectors, but no angle
 Fig 5-5, pg 123

Angle of resultant vector
 q = tan-1 (Ry/Rx)
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, mk
 Ff,k = mkFN

Static friction is similar
 Coefficient of static friction, ms
 Ff,s ≤ msFN
5.3 Force and Motion in 2D

System in equilibrium when Fnet = 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 136-137
 Inclined plane lab, pg 136-137

Revise friction lab to make it only friction
– different surfaces
 Revise inclined plane lab to make it
multiple angles for same surface
