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Forces
Chapter 6
Pg. 117-147
6.1: Force and Motion
 Objectives
 Define a force
 Differentiate between contact and long-range
forces
 Recognize the significance of Newton’s 2nd law of
motion and use it to solve problems
 Explain Newton’s 1st law and use it to describe
objects at equilibrium.
Force and Motion
 Force – a push or pull on a object
 The object is known as the “system”
 The world around the object is the
“environment”
 “F” is used to represent the magnitude or size of
the force.
 HOW MANY FORCES CAN YOU NAME?
Contact vs. Long-Range Forces
 Contact forces act on objects only when they
come into contact with the object.
 They have to be touching the object.
 Friction is a contact force.
 Long-range forces can act on objects without
having contact.
 Magnetic force is an example
 Force of Gravity – long-range force that acts on
all objects.
 Attracts forces to each other.
Forces have Agents
 Each force has an identifiable cause called an “agent”
 This is essentially what is is causing the force; if you cannot
name the agent, the force does not exist.
 What is the agent of a ball falling to the ground?
 The first step to solving any problem is creating a force
diagram or pictorial model of the event.
 We need to identify the system, the environment and all
the forces acting upon the system. Some will be contact
forces, some will be long-range or constant forces as well
Forces have Agents
 Drawing pictorial models
 Identify the system and circle it
 Identify every place the system and environment are
touching.
 Identify the contact forces
 Identify the long-range forces
 Replace object in model with a dot
 Use arrows to represent the forces
 Length of the arrow should equal magnitude of the
force.
 Label the forces with “F” to identify the agent
 Try Practice Problem 1 on pg. 119
Newton’s 2nd Law of Motion
 States: The acceleration of an object equals the
net force on that object divided by its mass.
 Gravity and friction influence almost everything, so
if we can avoid those by performing experiments it
is helpful.
 The best way to do so is study horizontal forces
because gravity does not affect horizontal forces
 We can also perform the experiment with low friction
wheels, on ice, or another low friction surface.
Newton’s 2nd Law
 How do we exert a controlled force on an
object?
 Stretching object work well, like a rubber band.
The further you stretch the object, the greater
the force exerted.
 Look at figure 6.2a on pg. 120 of the text.
 Determine acceleration of the object in 6.2b,
but calculating the slope of the graph.
How Acceleration Depends on Force
 You could repeat the experiment of the rubber band
and low friction cart and continue to stretch the
rubber band further.
 You can still determine the acceleration of the object
no matter the stretch.
 The force and acceleration are proportional and
create a linear relationship.
 The larger the force the greater the acceleration
 F = ka
 Force = k (slope of line) x acceleration
How Does Acceleration Depend on the Object
 What happens if we increase mass of the object
the force is being exerted on by 2-fold? 3-fold?
 You will find that if we double the mass of the
object the acceleration will become ½ of what it
was originally. This is because
 Force = mass x acceleration or F=ma
 This concept is simple: The heavier an object, the
more force it takes to move it.
Combining Forces
 What happens when we have more than once force
exerting a push/pull on an object?
 Forces can act in the same direction, in opposite
directions, and at directions that are angles of each
other.
 We should use a free-body diagram to draw multiple
forces
 A free-body diagram uses a dot with vectors drawn in
the direction of the individual forces
 Look at Figure 6-4 to see examples
Combining Forces
 The total force is always equal to the sum of all
the individual forces acting upon the object.
 The sum of 2 or more forces is called the net
force.
 The net force is the key:
 A = Fnet / m
Measuring Force: The Newton
 The Newton (N) is the net unit of force
 1 Newton is 1kgm/s2
 F =ma :
m =kg
a = m/s2
 Solve Practice Problems 2-6 on pg. 122
Newton’s 1st Law of Motion
 An object at rest will stay at rest unless acted upon by a
force.
 An object in motion will stay in motion (in a straight line at a
constant speed) unless acted upon by a force
 These two statements make up Newton’s 1st Law of Motion.
 But wait…….this does not always happen on Earth does it?
 NOPE!!!! Why? Because we are constantly being acted upon
by a variety of forces that you do not even know about .
Inertia
 Newton’s 1st law is often called the “law of
inertia”
 Inertia is the tendency of an object to resist
change.
 Things at rest want to stay resting
 Things moving want to stay moving
Equilibrium
 If the sum of the forces on an object equal zero then the
object is at equilibrium.
 Two states of equilibrium:
 Object is at rest
 Object is moving at a constant velocity
 Remember Rest is simply a special case of constant velocity = 0
 Newton’s 1st law defines net forces as anything that
disrupts an objects equilibrium
 Common sense: it is something that changes an objects
velocity
Physical Models: Free-Body Diagrams
 Look at Table 6-2 on pg. 123
 This table shows a variety of forces and how they
are defined. KNOW THEM!!!!!
 These forces are added, subtracted, etc to
determine net force.
 BEING ABLE TO DRAW FORCE DIAGRAMS IS
HUGELY IMPORTANT!!!!!!!!!!!!!!!!!!
 Try to draw force diagrams for Practice Problems 7-
11 on pg. 124
Common Misconceptions about Forces
 Friction dominates our world, so Newton’s laws are
hard to visualize.
 Also, some every day words are also used
interchangeably with words from physics; this causes
issues:
 When you throw a ball, the force of the hand remains
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on the ball
Forces are needed to keep an object moving
Inertia is a force
Air does not exert a force
The quantity ma is a force
Assignment
 6.1 Review
 Pg. 125
 Questions 1-5
 Will grade tomorrow.
6.2: Using Newton’s Laws
 Objectives
 Describe how the weight and the mass of an object
are related
 Differentiate between the gravitational force weight
and what is experienced as apparent weight.
 Define the friction force
 Distinguish between static and kinetic friction
 Describe simple harmonic motion
 Explain how the acceleration due to gravity
influences motion
Using Newton’s 2nd Law
 Aristotle believed the heavier the object, the
faster it falls.
 Galileo understood this, but knew to understand
true motion, we must ignore certain factors,
mainly air resistance/drag.
 We are trying to understand the forces that
causes objects to fall/ move, so we ignore
certain “Earth” factors.
Mass and Weight
 No evidence Galileo actually dropped two balls
from the Tower of Pisa (yes the leaning one), but
his theory is very simple.
 He said that if Aristotle was correct then dropping
two cannon balls from a given height would result
in both falling at the same rate, however fastening
them together and dropping them would result in
them falling at 2x the first rate.
 Galileo said that this was incorrect and theorized
that all object in free fall gain speed at the same
rate, no matter what their weight is.
 We now know this to be true and the force that
causes this acceleration is GRAVITY
Mass and Weight
 The simplest way to picture the force of gravity
(Fg) is to use Newton’s 2nd law (F= ma)
 For gravity this gives us Fg = mg
 The direction of both components is downward
 This means the magnitude of the force is equal to
the force times the acceleration, which we also
call weight
 This hold true on Earth at 9.8m/s2, but the force of
gravity is different on different planets
Scales
 Measure weight or the force you are exerting
downward.
 Old scales use springs to counteract your force
and then that is read by the scale.
 New scales have sensors that do this exact same
thing
 This means your weight would be different on
other planets because of the difference in the
force of gravity
Force and Motion Problem Solving
1. Read the problem carefully. Visualize the situation and
2.
3.
4.
5.
6.
7.
8.
create a pictorial model
Circle the system and choose your coordinate system
Decide what quantities are known (givens) and which
quantities you need to find (unknown). Assign symbols to
your unknown.
Create a motion diagram that shows the direction of the
force and create a free-body diagram that shows the net
force on the object
Use Newton’s laws to link acceleration and net force
Rearrange the equation to solve for a or F(net). Newton’s
2nd law uses vectors so it must be solved using X and Y
directions
Substitute the given quantities with their units in the
equation and solve
Check your results to make sure they make sense
Example Problems
 P. 128 and 129 of textbook
 Try Practice Problems on pg. 129 (12 and 13) on
your own.
Apparent Weight
 The force exerted by the scale is measuring
apparent weight.
 What happens if you stand one foot on and one
foot off the scale? What happens in the elevator
scenarios?
 What happens if the cable holding the elevator
breaks and the acceleration is equal to – g?
 The scale would show your weight as zero.
 Does that mean you actually weigh nothing?
 No, it means there are no contact forces pushing up
on you.
The Friction Force
 Friction is the contact force that opposed
motion.
 You attempt to push a large, heavy box across
the floor. The laws of physic say that the box
should move, but it does not move. Why?
 You push harder, the box still does not move; this
means some force must exist between the box
and the surface it is sitting on to counteract the
force you are exerting on the box.
 This force is called the Static Friction Force
 This force acts in response to other forces
Static and Kinetic Friction
 Finally you push hard enough for the box to
move; I guess we overcame friction……
 Not so fast, friction is still at play
 What happens when you stop pushing the box?
 The box stops moving? It slides a little bit then stops
moving?
 This force that acts between two objects
(surfaces) that are in relative motion is called the
Kinetic Friction Force
A Model for Friction Forces
 Friction forces are Complicated, but we can simplify
them.
 The friction force is proportional to the magnitude of
the force pushing one surface against another.
 That force, perpendicular to the surface, is the
Normal force.
 The equation we use is:
 Force of Friction (kinetic) = kinetic coefficient of
friction times the Normal force
 Ffk = μkFN
A Model for Friction
 The static friction force relates to the normal
force using this expression:
 0≤ Ffs≥μsFN
 This tells you that the static friction force can
range from zero to μs (static friction coefficient)
times the Normal force.
 The static friction coefficient times the normal
force is the maximum friction force that can be
overcome, because higher than this the object
begins to move.
A Model for Friction
 The previous equations solve for the magnitude
of the forces only.
 The friction force and normal force are at right
angles to each other.
 Table 6-3 on pg. 131 shows several coefficients of
friction that we will use to solve upcoming
problems.
 Notice all listed coefficients are below 1.0 but that
does not mean that all possible coefficients are
below 1.0
Example Problems
 Look at Example Problems with Solutions on pg.
131-132
 Try to Solve Practice Problems 14-16
Causes of Friction
 All surfaces, no matter how smooth they appear,
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are rough at a microscopic level.
When you push an object across another object
the high points of the surfaces temporarily bond
You must break those bonds for the object to
move
This is the source of Static Friction
As the object moves, there are still electrostatic
attractions between the high points of the
surfaces; this causes weak kinetic friction.
Air Drag and Terminal Velocity
 As an object moves through air or a fluid, there is
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a friction-like force that exerted on that object.
The big difference is that with air and fluids, the
speed and shape of the object matter.
The larger the object, the faster it is moving, or
the more surface area = increase in the force.
This is Drag
When the drag force equals the force of gravity
results in a constant velocity known as Terminal
Velocity.
The more aerodynamic an object the greater
the possible terminal velocity
Periodic Motion
 Playground swings sway back and forth in the
same path, this is an example of vibrational
motion
 Other examples are a pendulum in a clock,
springs, and guitar strings.
 All of these have a zero, equilibrium point and
are pulled away from this zero point, then
restored to the zero point.
 When the force that restores equilibrium is
directly proportional to the displacement of the
object this is called Simple Harmonic Motion
Periodic Motion
 Simple harmonic motion has 2 quantities
represented
 T – the period
 The period is the time needed to complete one
cycle of motion.
 Amplitude
 Amplitude is the maximum distance the object
moves from the zero (equilibrium) point.
Mass on a Spring
 Picture an object dangling from a spring
 Two forces are exerted on this object: the downward
force of gravity and the upward force of the spring, which
depends on how much the spring is stretched.
 Springs obey Hooke’s law
 The spring will work to match the force of the object it is
connected to, thus putting the object at equilibrium.
 When we pull the object down, the spring will produce an
upward force
 When we push the object up, the spring will produce a
downward force.
Mass on a Spring
 The further the spring is stretched or compressed,
the stronger the restoring force exerted by the
spring.
 Now when released, does the block just return
back to equilibrium?
 No, inertia is too great causing the object to move
past it’s equilibrium point and either compress or
stretch the spring temporarily. This restarts the
process.
 The period of vibration/oscillation “T” depends on
the mass of the object and the strength of the
spring, but not on the amplitude of the motion
Pendulum
 Contains two parts: the bob (heavy end mass)
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and the rod/string with a length “l”
The bob is pulled to one side, when released, the
bob swings back and forth.
A force of “T” is exerted by the rod and gravity
exerts a force on the bob
The sum of these two forces: FT and Fg produces
the net force.
The net force is always restoring, thus acting in
the opposite direction of the displacement of
the bob.
Pendulum
 When the angle is small, the motion is linear and
thus simple harmonic motion.
 The period of a pendulum of length “L” is given
as:

T = 2π √l/g
 The period depends only on the length of the
rod and the acceleration due to gravity, not on
the mass of the bob
Resonance
 Mechanical resonance is the addition of small
forces to a vibrating/oscillating object that will
increase the amplitude
 The time interval for application of forces is equal
to the period of oscillation
 What the??
 Think of this…..you are on a swing, how do you
make the swing to higher and higher??
 You pump your legs and the highest points the
swing reaches……this is resonance
Assignment
 6.2 Section Review
 Questions 1-5
 Pg. 136 of textbook
 Due next class
6.3: Interaction Forces
 Objectives:
 Explain the meaning of interaction pairs of forces
and how they are related by Newton’s third law
 List the four fundamental forces
 Draw the environment in which each fundamental
force can be observed.
 Explain the tension in ropes and strings in terms of
Newton’s third law
Identifying Interaction Forces
 Certain forces will be dependent on other
forces: Think of playing catch. A baseball is
thrown with a force, then the person catching it
exerts a force on the ball with his/her glove to
stop it. The ball strikes with force, and has a force
exerted on it by the glove.
 We will now bring the environment into play and
see how different forces interact.
Systems and the Environment
 So far, we have only looked at scenarios with a single
system (object).
 What we will examine now are situations that have two
systems that are interacting upon each other.
 Remember the system is the object effected by a force
 The environment is everything around that object that is
not the system.
 Think back to the playing catch scenario…what are the
systems? What are the forces interacting upon them?
Newton’s Third Law
 Interaction pair – two forces that are in opposite directions
and have equal magnitude.
 The forces of playing catch: F –ball on glove and F – glove
on ball are interaction pairs.
 These forces summarize Newton’s Third Law of Motion; states
“all forces come in pairs and that the forces in pairs act
upon different objects that are of equal magnitude and in
opposite directions
 Read pg. 139 to yourself: Car on Road Scenario.
Problem Solving Strategy
1. Separate the Systems from the Environment
2. Draw a Pictorial Model with coordinate systems
3.
4.
5.
6.
for each system and draw a physical model
which includes free-body diagrams for each
system.
Connect interaction pairs with dashed lines
Use Newton’s 2nd law to relate net force and
acceleration for each system.
Newton’s 3rd law equates the magnitudes of the
force pairs and gives relative directions
Solve the problems and check units, signs and
magnitude to make sure they make sense.
Example Problem
 Look at Example Problem on pg.140-141
 Try Practice Problems 20-21 on your own
Four Fundamental Forces
 Gravitational Interaction
 Based on the attraction between two objects due to the
mass of the objects
 Electromagnetic Interaction
 Magnetic forces and electric forces
 Holds atoms and molecules together
 Responsible for all contact forces
 Strong Nuclear Interaction
 Acts between protons and neutrons in nuclei
 Weak Nuclear Interaction
 Responsible for radioactive decay
 http://www.neok12.com/video/Types-ofForces/zX747d7003674a6f79434459.htm
Assignment
 Read Chapter 6, Section 3
 Will attempt to finish the section tomorrow
Forces of Ropes and Strings
 We have already touched on tension but let us
discuss some more so we can relate it to Newton’s
3rd Law of Motion.
 Say we have a rope that is attached to a
bucket. At a certain force the rope will break,
however up to that point it means we have
forces holding the rope together.
 Now we bring in Newton….What is means is that
there is a Force that the top of the rope exerts on
the bottom of the rope and a Force that the
bottom of the rope exerts on the top of the rope
 This gives us 2 opposing forces so it obeys Newton’s
3rd Law
Forces of Ropes and Strings
 The origin of tension is, of course, electromagnetic and
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the result of attraction between the molecules and
atoms of the rope.
The tension of the ropes is measurable, but the bucket is
not moving so it is in equilibrium.
This means that the two interaction forces of the rope
are pulling in opposite directions at the same
magnitude.
This means that the Force of Tension (top on bottom) –
the force of gravity = 0
Or that the Force of Tension (top on bottom) = Force of
Gravity
Force of Ropes and Strings
 Tension is also at work in a Tug-of-War.
 Two teams are pulling in opposite directions.
 If both forces are equal than the rope will not move.
 Now what is the Tension on the rope??
 To figure this out we have to divide the rope into two halves:
Left and Right
 Neither side is moving so this means the net force on both
sides is 0. They are interaction pairs so they must be equal
and opposite, this means the tension in the rope is equals the
force with which each team pulled
Assignment
 6.3 Review
 Pg. 143
 Questions 1-3
 Due Next Class