1. CHAPTER 3
RELATIVE VELOCITY

2. FRAMES OF REFERENCE
• Velocity measurements differ in
different frames of reference.
• Observers using different frames of
reference would generally not agree
on some features of motion.

3. RELATIVE VELOCITY
• Write down all information that was
given in the problem and that you
want to know in the forms of
velocities with some kind of
subscript.

4. EXAMPLE PG 108 SAMPLE 3F
A boat heading north crosses a wide river
with a velocity of 10 km/hr relative to the
water. The river has a uniform velocity of
5.0 km/hr due east. Determine the boat’s
velocity with respect to an observer on the
shore.

5. YOU TRY!
(pg 109 #1)
A passenger at the rear of a train traveling
at 15 m/s relative to Earth throws a baseball
with a speed of 15 m/s in the direction
opposite the motion of the train. What is
the velocity of the baseball relative to Earth
as it leaves the throwers hand?

6. CHAPTER 4
FORCES & LAWS OF MOTION

7. 4.1: CHANGES IN MOTION
• Force: a push or pull exerted on an
object.
• Forces cause a change in velocity.
• Force is a VECTOR QUANTITY.
• SI unit of force is the Newton (N).
• Forces can act through contact or at a
distance

8. CONTACT VS FIELD FORCES
• Contact Forces – result from physical
contact between two objects
• Usually easy to identify
• A physical push or a pull
• Field Forces – do not involve physical
contact between two objects
• Example: Electric Force, GRAVITY!!! 

9. FBD: FREE BODY DIAGRAMS
• Helps analyze a situation
• Isolate an object and the forces acting
on that object.
• FBDs are used to show all the external
forces acting on an object.

10. HOW TO FBD
1. Draw your object as single point. (forces are
assumed to act on a single point at the center of an object)
2. Draw and label vector arrows representing
all external forces acting on the object.
3. Make sure you are only drawing the forces
acting on the object and NOT the forces that
the object acts on other things.
4. When finished, an FBD can be used to find
the net external force on an object.

11. THE MASTERMIND
• In the 1630s, GALILEO – yes not Newton
– realized that a block sliding on a
perfectly smooth surface would slide
forever in the absence of an applied
force.

12. NEWTON
• In 1687, Newton further developed the
concepts that were initially developed by
Galileo which has now come to be known
as Newton’s 1st Law of Motion

13. NEWTON’S FIRST LAW
An object at rest remains at
rest, and an object in
motion stays in motion,
unless acted upon by an
outside force.

14. LAW OF INERTIA
• Newton’s 1st Law came to be known as
the “Law of Inertia”
• Inertia = tendency of an object to not
accelerate
• The more mass something has, the
harder it is to …
• Slow it down …if it is already moving
• Get it to start moving … if it is at rest

15. WEIGHT VS. MASS
• Mass = the amount of matter something
has.
• Weight = the magnitude of the force of
gravity acting on an object.
**You need mass to calculate weight.
MASS ≠ WEIGHT

16. THE FORCE OF GRAVITY
• The force of gravity as we talk about it in
everyday life is called WEIGHT.
• We will call the force of gravity Fg.
• We can calculate the force of gravity
using the following formula.
Fg= mg
Fg= Force of Gravity, measured in Newtons
m= mass, measured in Kilograms
g= acceleration due to gravity, -9.8 m/s2

17. EXAMPLE
A bag of sugar has a mass of 2.26 kg. What
is its weight?

18. YOU TRY!
If a the mass of Mickey Mouse is 24 kg. Calculate
Mickey’s weight on Earth.

19. THE NORMAL FORCE
• The Normal Force= a force exerted by
one object on another in a direction
perpendicular to the surface of contact.
FN
Fg

20. EXAMPLE
A block of mass 26 kg is sitting stationary on a 1 m high
table. Calculate the block’s weight and normal force.

21. DO NOW
A 2.26 kg book is dropped from a height of
1.5 m.
a.) What is the book’s acceleration?
b.) What is its weight in Newtons?

22. CALCULATING NET FORCE
In order to calculate the net force we must first do the
following …
1. Identify a coordinate system
2. Draw a FBD of the system
3. Draw a chart breaking up our forces
4. Add all the forces in the x-direction set them equal to the
“net force”
5. Repeat step three for the y-direction.

23. EXAMPLE
A crate is pulled to the right with a force of 82 N, to the left
with a force of 115 N, upward with a force of 565 N and
downward with a force of 236 N.
a.) Find the net external force in the x direction
b.) Find the net external force in the y direction
c.) Find the magnitude and direction of the net external force
on the crate.

24. EXAMPLE 2
Derek leaves his physics book on top of a drafting table that
is inclined at 35 degrees. The free body diagram (on the
board) shows the forces acting on the book. Find the net
external force acting on the book, determine whether the
book will remain at rest in this position.

25. YOU TRY
INDEPENDENTLY:
Work on 1, 3 & 4 on pg. 133

26. NEWTONS 2ND LAW
Force is proportional to mass and
acceleration.
Newton’s 2nd Law relates Force, Mass and
Acceleration

27. NEWTONS 2ND LAW
The acceleration of an object is directly
proportional to the net external force acting
on the object and inversely proportional to
an object’s mass.
To put it more simply …
ΣF=ma

28. EXAMPLE
Roberto and Laura are studying across from each other at a
wide table. Laura slides a 2.2 kg book toward Roberto. If the
net external force acting on the book is 2.6 N to the
right, what is the book’s acceleration?

29. YOU TRY
The net eternal force on the propeller of a
3.2 kg model airplane is 7.0 N forward.
What is the acceleration of the airplane?

30. NEWTON’S 3RD LAW
• Forces always exist in pairs
• When two objects interact with one
another, the forces they mutually exert
on each other are called an action-
reaction pair.

31. NEWTON’S 3RD LAW
For every action there is an
equal and opposite
reaction.

32. NEWTON’S 3RD LAW
• Action and reaction forces each act on different
objects.
• Field forces also exist in pairs.

33. ACTION REACTION EXAMPLE 1
WHAT IS THE ACCELERATION OF THE SYSTEM?
WHAT IS THE FORCE BOX 1 PROVIDES ON BOX 2?
WHAT ABOUT BOX 2 ON BOX 1?

34. ACTION REACTION EXAMPLE
BOX 1 HAS A MASS OF 30KG
BOX 2 HAS A WEIGHT OF 196N
THE FORCE IS 100 NEWTON'S
WHAT IS THE ACCELERATION OF THE SYSTEM?
WHAT IS THE FORCE BETWEEN 1 AND 2?

35. CONNECTED MASS
EXAMPLE 1
IF BLOCK ONE HAS A MASS
OF 20 KG AND BLOCK 2
HAS A MASS OF 35 KG
WHAT IS THE
ACCELERATION OF THE
SYSTEM?

36. CONNECTED MASS EXAMPLE 2
IF BLOCK ONE HAS A MASS OF 10 KG, BLOCK 2
HAS A MASS OF 15 KG, AND BLOCK 3 HAS A MASS
OF 20KG WHAT IS THE ACCELERATION OF THE
SYSTEM? IGNORE FRICTION

37. FRICTION
• Friction ALWAYS opposes motion – always in
the opposite direction of the NET FORCE.
• There are two different types of friction: Static
Friction & Kinetic Friction

38. STATIC FRICTION
• The resistive force that keeps an object from
moving.
• Usually, the static friction of the object is equal
to in magnitude but opposite in direction to the
applied force.

39. KINETIC FRICTION
• The retarding frictional force on an object in
motion is called the force of kinetic friction.
• Kinetic frictional forces arise from complex
interactions at the microscopic level between
contacting surfaces.

40. CALCULATING FRICTION
• The force of friction is proportional to the normal
force.
• Friction also depends upon the surfaces in
contact.
• The force of friction depends upon the
composition and qualities of the surfaces in
contact.
• The quantity that expresses the dependence of
frictional forces on the particular surfaces in
contact is called the coefficient of friction.

41. CALCULATING FRICTION
Ff=μFn
Ff= Force of Friction
μ= coefficient of friction
Fn = Normal Force

42. COEFFICIENT OF FRICTION
μk= coefficient of kinetic
friction
μs= coefficient of static
friction

43. EXAMPLE
A 24 kg crate initially at rest on a horizontal
floor requires a 75 N horizontal force to set
it in motion. Find the coefficient of static
friction between the crate and the floor.

44. YOU TRY
• A 25 kg chair initially at rest on a horizontal floor
requires a 365 N horizontal force to set it in
motion. Once the chair is in motion, a 327 N
horizontal force keeps it moving at a constant
velocity.
A. Find the coefficient of static friction between
the chair and the floor
B. Find the coefficient of kinetic friction between
the chair and the floor

45. ELEVATOR PROBLEM