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Honors Physics
Glencoe, 2005
When working in more than one dimension (linear system), we
need to revisit some trigonometry
Pythagorean Theorem a2+b2=c2
 a and b are the sides of a right triangle
 c is the hypotenuse (or resultant)
Law of Cosines
 a and b are the sides of any triangle
 q is the angle between a and b
 R is the resultant
Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
 a, b and c are the sides of any triangle
 A, B and C are the angles opposite sides a, b and c, respectively
A car is driven 125.0km due west, then 65.0km
south. What is the magnitude of its displacement?
Solve the problem graphically and mathematically
and check your answer against each other.
An ant is crawling on the sidewalk. At one
moment, it is moving south a distance of 5.0mm. It
then turns southwest and crawls 4.0mm. What is
the magnitude of the ants displacement?
Vector Resolution- breaking down into its vertical and
horizontal parts
 sin(q) = opposite/hypotenuse = ay/a
 cos(q) = adjacent/hypotenuse = ax/a
 tan(q) = opposite/adjacent = ay/ax
Solving for individual sides
 ax= (a)cos(q)
 ay= (a)sin(q)
If you have more than two vectors, you don’t need
to resolve them all before you add them!
 Use the Tail-To-Tip method and resolve the resultant
 Angle of Resultant
A GPS receiver indicates that
your home is 15.0 km and 40.0°
N of W, but the only path
through the woods leads
directly north. If you follow the
path 5.0 km before it opens
into a field, how far, and in
what direction, would you have
to walk to reach your home?
Toprameneesha walks 0.40 km in a direction 60.0°
W of N, then goes 0.50 km due west. What is his
Kinetic Friction- friction in motion (v>0 m/s)
 When velocity is constant, a=0 m/s2, therefore Fnet=0 N
▪ Kinetic Friction = Applied Force
Static Friction- friction that occurs before the
object moves (v=0 m/s)
 Before an object has moved, the static friction equals
the applied force
 Similar to FN: Ff, static is only as big as it needs to be, to a
particular maximum
Before touching the couch, Ff, static is o N
When applying 1N of force, Ff, static is 1N
When applying just enough force to start the couch
moving, Ff, static reaches its maximum
 Ff, static‘s maximum is based on surface irregularities
When moving at a constant velocity, the applied
force equals the Ff, kinetic
Each object has unique surface irregularities, which
determines the frictional forces
 The results of these interactions is the coefficient of
static and kinetic friction (ms, mk)
The frictional force is based on this coefficient and
how hard the surface is holding the object up (FN)
Kinetic Friction
Ff, kinetic=mkFN
Static Friction
Ff, static≤msFN
See Figure 5-10
A girl exerts a 36N horizontal force as she pulls a
52N sled across a cement sidewalk at a constant
speed. What is the coefficient of kinetic friction
between the sidewalk and the metal sled runners?
Ignore air resistance.
You help your mom move a 41kg bookcase to a
different place in the living room. If you push with a
force of 65N and the bookcase accelerates at
0.12m/s2, what is the coefficient of kinetic friction
between the bookcase and the carpet?
Equilibrium- when all forces balance/cancel each
other out
 Net force is zero
 Acceleration is zero
 Velocity is constant (even if it’s zero)
Equilibrant- the additional force needed to cancel
out a force or group of forces
 For two forces acting, it would be the opposite of the
resultant of the triangle
Find the equilibrant for the following forces.
Page 132
There are several forces interacting when working
with slopes and incline planes.
 Fg, FN, Ff, kinetic (or Ff, static)
 We need to use our trig properties to address these
An ant climbs at a steady speed up the side of its
anthill, which is inclined at 30° from the vertical.
Sketch a free body diagram for the ant.
Kohana, who has a mass of
50.0 kg, is at the dentists
office having her teeth
cleaned. If the only
component of her weight
perpendicular to the plane of
the seat of the chair is 449N,
at what angle is the chair