Unit 3:
Newton’s Laws
Chapter 4 & 5
Unit 3 Objectives
1.
Describe and give examples of Newton's 1st Law.

2.
Understand and apply Newton’s 2nd Law


3.
Newton's 1st Law: Objects at rest stay at rest, objects in motion stay
in motion at constant speed in a straight line unless acted upon by
unbalanced forces.
Newton's 2nd Law: The acceleration of an object is directly
proportional to the net force on an object and inversely proportional to
the mass of the object (a = ΣF/m or ΣF = ma).
Use Newton's 2nd Law to qualitatively describe the relationship
between m and a, F and a, m and F. (For example, if you double the
mass, the acceleration will . . ?)
Understand and apply Newton's 3rd Law. Recognize that all
forces come in pairs; paired forces are equal in magnitude, but
opposite in direction. FAB = -FBA

Newton's 3rd Law: For every force, there is an equal and opposite
force. Another way of thinking about Newton's third law: You can't
touch without being touched and you can only touch as hard as you
are touched.
Unit 3 Objectives
4.
Given a diagram or a written description of the forces acting on an
object:




5.
Draw and label a force diagram for the object
Choose the simplest coordinate axis for analysis: horizontal – vertical or
parallel – perpendicular
Break forces in x and y components using trigonometry
State whether the velocity of the object is constant or changing
Solve quantitative problems involving forces, mass and acceleration using
Newton's 2nd Law.





use force diagram analysis in order to determine the equation for the forces
acting on an object in a particular direction.
Use Newton's second law to determine an object's acceleration and/or missing
force.
Use kinematics to determine the acceleration needed to be used in Newton’s
second law. Use Newton’s second law to determine the acceleration needed
in a kinematic calculation.
Interpret graphs of position-time, velocity-time, acceleration-time and relate
them to the net force acting on the object and vice-versa
Use derivatives and integrals to for part c when the acceleration is not
constant.
Unit 3 Objectives
6.
Distinguish between static and kinetic friction and qualitatively describe
what factors affect it.


Apply the model of static friction to an object at rest (or on the verge of moving)
in order to determine the maximum static friction force or coefficient of static
friction for two surfaces.
Apply the model of kinetic friction to an object moving at constant speed or
accelerating in order to determine the kinetic friction force or coefficient of
kinetic friction of two surfaces.
7.
Distinguish between the mass of an object and the force of gravity acting
on it, aka weight.
8.
Recognize that forces are classified as either contact and non-contact
forces. Also, be able to distinguish which of the four fundamental forces a
particular force is.
9.
For an object moving where drag is a factor:



Draw the graphs of y vs. t, v vs. t, and a vs. t and understand the basic
features of the graph
Determine the terminal velocity of the object recognizing that the acceleration
is zero
Express Newton’s second law in differential form
Forces


A push or a pull
Forces must act on an object




Pushes or pulls must be applied
to an object
Forces do not exist in isolation
from the object
Forces require agents:
something to do the pushing
or pulling
Unbalanced forces cause an
object to accelerate….



To speed up
To slow down
To change direction
Contact versus Field Forces
CONTACT
 Forces that exist during physical contact




Tension
Friction
Applied Force
Normal
FIELD FORCES
 Forces that exist with NO physical contact


Gravitational
Electromagnetic
Sir Isaac Newton 1642-1727

Why do objects accelerate?



Before Newton, people that studied
motion believed that an internal
property of objects is what caused
this acceleration.
Force was required to keep objects
moving
Newton, however, rejected this
belief.


The nature of objects is to continue
moving unless some force acts on
them.
From Galileo’s Thought Experiment
Galileo’s Thought Experiment
Galileo’s Thought Experiment

This thought experiment lead to Newton’s
First Law.
Newton’s First Law

Every body perseveres
in its state of being at
rest or of moving
uniformly straight
forward except insofar
as it is compelled to
change by forces
impressed.
Newton’s First Law

An object in motion remains in motion in a straight line and
at a constant speed or an object at rest remains at rest,
UNLESS acted upon by an EXTERNAL (unbalanced) Force.



Condition #1 – the object CAN move but must be at a CONSTANT
SPEED
Condition #2 – The object is at REST
Constraint – As long as the forces are BALANCED!!!
 All the forces are balanced

SUM of all the forces are ZERO
BOTTOM LINE: There is NO ACCELERATION in
this case, and the object must be in equilibrium.
Forces & Equilibrium

If the net force (ΣF) on a body is zero, then it is
in equilibrium
 Forces are balanced
 No distinction between
objects that have no forces
acting on them or objects on
which the sum of external
forces are zero
Dynamic Equilibrium
 An
object in equilibrium
may be moving relative to us

Static Equilibrium
 An
object in equilibrium may
appear to be at rest
What if NOT in Equilibrium?

If an object is NOT at rest
nor is it moving at a constant
velocity, then there must be
UNBALANCED FORCES
acting on the object.
 One
force(s) in a certain direction
overpowers the others
Newton’s First Law – Law of Inertia

INERTIA – a quantity of matter, also called
mass
 Italian
for “lazy”
 Resistance to change

MASS – same thing as inertia (to a physicist)
 Measured
in kilograms
Free Body Diagrams (FBD)

A pictorial representation of forces complete with labels!
Free body Diagrams
Can choose to have the coordinate
axis as horizontal-vertical or as
parallel-perpendicular to the surface!!!
Inertial Reference Frames

Reference Frame
 The
part of the world that we use to measure motion
of moving objects
 Since the world around us seems to be at rest
(uniform), then any motion we measure relative to our
surroundings is correctly observed


If motion appears uniform, it must truly be uniform, and if the
motion appears nonuniform, then it must truly be nonuniform.
What if instead of using the world around us
(uniform motion), we used a moving car (nonuniform motion)?
Inertial Reference Frames

EXAMPLE: You are a passenger riding in a car.
Brakes are applied, and the book on the seat
next to you slides forward.
 No

apparent force on the book, yet it moved
Violates Newton’s First Law
 Your
friend standing on the side of the road, sees
you, the car, and the book moving together

Follows Newton’s First Law
Inertial Reference Frames

Galileo
 in
all frames of reference which are moving
uniformly relative to each other, the laws of
nature must be the same
 Reference frames are not accelerating !!!

Classical mechanics only hold true in
inertial reference frames!!!
Mass & Weight

MASS - A property of an object that
determines how much it will resist a
change in velocity
 Measured

in kilograms
WEIGHT – a force due to gravity
 How
your mass is affected by gravity
F g  mg
 NOTE:
MASS and WEIGHT are NOT the same
thing. Mass never changes while weight does as
gravity changes.
Newton’s Second Law
“A change in motion is proportional to the motive
force impressed and takes place along the straight
line in which that force is impressed.”

A body acted on by an external
force will accelerate

acceleration is directly
proportional to the net force on
an object and inversely
proportional to its mass.
Newton’s Second Law
Slope = mass
Acceleration is directly proportional to Force. Thus the resulting
acceleration-force graph is linear with y-intercept at the origin.
Newton’s Second Law
Acceleration is inversely proportional to mass. Thus the resulting
acceleration-mass graph is a inverse (hyperbola).
Example: Rocket Guy

Rocket Guy weighs 905 N and his jet pack
provides 1250 N of thrust, straight up.
What is his acceleration?
FThrust
Fg = mg
ΣF = ma
Fthrust – Fg = ma
1250– 905 = 92.3 a
a = 3.74 m/s2
Fg
905 N = m (9.8m/s2)
m = 92.3 kg
Practice: Helicopter Lift

A helicopter of mass 3770 kg can create an upward lift
force F. When empty, it can accelerate straight upward
at a maximum of 1.37 m/s2. A careless crewman
overloads the helicopter so that it is just unable to lift
off. What is the mass of the cargo?
Example Problem

A 10 kg box is being pulled across the
table to the right at a constant speed with
a force of 50 N.
 Calculate
the Force of Friction
 Calculate
the Normal Force
Example Problem Continued

Suppose the same box is now pulled at an angle of 30
degrees above the horizontal at constant speed.


Calculate the new Frictional force
Calculate the new Normal Force
Newton’s Second Law: Systems

Instead of treating the problem as two separate
objects, treat as one system.
1. Draw a FBD for each object in the system.
2. Only forces parallel to the acceleration of
the individual object affect the motion
3. Forces perpendicular to motion do not
affect it
4. Internal forces do not affect motion (only
external)
5. Forces that point in the direction of motion
are positive
6. Forces that point away from direction of
motion are negative
a
a
Example: Systems

A mass, m1 = 3.00 kg, is resting on a frictionless horizontal table is
connected to a cable that passes over a pulley and then is fastened
to a hanging mass, m2 = 11.00 kg as shown below. Find the
acceleration of each mass and the tension in the cable.
Newton’s Third Law
“To any action there is always an opposite and equal reaction; in other
words, the actions of two bodies upon each other are always equal and
always opposite in direction”.
For every action, there is an
EQUAL and OPPOSITE reaction!!
Action-Reaction
Pairs
1.5 N
Newton’s Third Law Examples
This law focuses on action/reaction pairs
(forces)
They NEVER cancel out
Action: HAMMER HITS NAIL
Reaction: NAIL HITS HAMMER
Action: Earth pulls on YOU
Reaction: YOU pull on the earth
Friction

A force that resists the motion of one
object sliding past another
 Always
parallel to the surface
Note: Friction ONLY depends on the
MATERIALS sliding against
each other, NOT on surface area.
Friction: Two Types

Static
 Friction
that keeps an object at rest and
prevents it from moving

Kinetic
 Friction
that acts during motion
The coefficient of
friction is a unitless
constant that is
specific to the
material type and
usually less than
one.
Static Friction

A force that resists the sliding motion of two objects that
are stationary relative to one another.



Frictional force must be calculated by applying Newton’s 2nd Law
Equation for static friction is for the maximum value
Coefficients of friction have been determined for different
material surfaces
Kinetic Friction

Friction when an object slides along
another.
Friction: Example


A 1500 N crate is being pushed across a level floor at a constant
speed by a force F of 600 N at an angle of 20°below the horizontal
as shown in the figure.
a) What is the coefficient of kinetic friction between the crate and the
floor?
Inclines




Rotate axis to make it parallel and
perpendicular to the surface
Break weight into components
Write equations of motion or
equilibrium
Solve
Inclines: Example
Masses m1 = 4.00 kg and m2 = 9.00 kg are connected by a light string that passes
over a frictionless pulley. As shown in the diagram, m1 is held at rest on the floor
and m2 rests on a fixed incline of angle 40 degrees. The masses are released from
rest, and m2 slides1.00 m down the incline in 4 seconds. Determine
(a) The acceleration of each mass
(b) The coefficient of kinetic friction
(c) The tension in the string.