Download Changes in Motion Force

Forces and the
Laws of Motion 1
Section 1: Changes in Motion
Force: push or a pull
 causes changes in motion
 describes the interactions between an object and its
environment
A force can cause an object’s velocity with respect to time
(acceleration)
 moving from stationary
 stopping
 changing direction
SI unit for force = Newton (N)
 Amount of force necessary when acting on a 1 kg mass to
produce an acceleration of 1 m/s2
 1 N = 1 kg x 1 m/s2 = kg·m/s2
 Weight of an object is the measure of the gravitational force
exerted on that object
o Interaction of an object’s mass with the gravitational
field of another object (Earth)
o 1 lb = 4.45 N
o 1N = .225 lb
Forces can act through contact or at a distance
Contact forces: forces that result from physical contact
between two objects
 push, pull (in softball – throwing, hitting, or fielding the
ball)
Field forces: forces that do not involve physical contact
 gravity
o masses create gravitational fields in the space
around them
o objects fall to the Earth because of the interaction
between the object’s mass and the Earth’s
gravitational field
 electromagnetic fields
o charged objects create electromagnetic fields
o attract or repel other objects (example static
electricity)
Macroscopic contact
forces are all due to
microscopic field
forces.
 Ex: contact
forces in a
collision are due
to electric fields
between atoms
and molecules
Forces and the
Laws of Motion 2
Force diagrams
Sample Problem A
Example: push a toy car, it accelerates. Push
the toy car harder and it accelerates faster.
 Acceleration depends on the magnitude
of the force
 Direction depends on the direction of the
force
 Force is a vector!
o Diagrams that show force vectors
as arrows are called force
diagrams.
The photograph shows a person pulling a
sled. Draw a free-body diagram for this
sled. The magnitudes of the forces acting
on the sled are 60 N by the string, 90 N by
the Earth (gravitational force) and 90 N
upward by the ground.
Drawing force diagrams
 Tail of the arrow is attached to the object
on which the force is acting
 Force vector points in the direction of the
force
 Length of the arrow is proportional to the
size (magnitude) of the force
 Assume all objects are point objects (all
mass is concentrated at a single point in the
center of the object)
Step 1: Identify the forces acting on the
object and the directions of the forces.
 String exerts 60 N in the direction of
the pulling
 Earth exerts a downward force of 90
N
 Ground exerts an upward force of 90
N
Free-body diagrams
Step 2: Draw a diagram to represent the
isolated object.
Free-body diagrams only show the forces
 acting ON the object itself
 nothing from the environment
 no forces exerted by the object
Step 3: Draw and label vector arrows for
all external forces acting on the object.
Forces and the
Laws of Motion 3
Section 2: Newton’s First Law
Force and motion
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A common misconception: an object on which no force is acting will always be at rest
True reality: if an object is moving at a constant velocity, then there is no net force
acting on it
o Block sliding on thick carpet
o Block sliding on a waxed floor
 A block moving on a perfectly smooth surface would slide forever in the
absence of an applied force
1630s – Galileo stated it is an object’s nature to maintain its state of motion or rest
Further developed by Sir Isaac Newton in 1687 and became known as Newton’s first
law of motion
Newton’s First Law
An object at rest remains at rest, and an
object in motion continues in motion with
constant velocity (constant speed in a
straight line) unless the object
experiences a net external force.
Sum of forces = net force
A car is traveling at a constant velocity.
 Many forces act on the car
 According to Newton’s 1st law of motion,
the net external force on the car must
equal zero.
Fforward: forward force of the road on the tires
Fresistance: acts in the opposite direction, is due to
friction and air resistance
Fgravity: downward gravitational force on the car
Fground-on-car: upward force on the car from the road
Inertia:
 Tendency of an object not to
accelerate (resist changes in its
motion)
 Newton’s 1st law is called “law of
inertia” because in the absence of a
net force, a body will preserve its
state of motion
o When the net external force on
an object is zero, the object’s
acceleration (or the change in
the object’s velocity) is zero.
Car will maintain its constant velocity as
long the vector sum of the applied forces
equals to zero.
Forces and the
Laws of Motion 4
External force:
 single force that acts on an object as the result of the interaction between the object
and its environment
o all 4 forces noted on the car are external forces
Net force:
Vector sum of all forces acting on an object
When all external forces are known, the net force can be determined by using the methods
for finding resultant vectors.
 Net force is equivalent to the one force that would produce the same effect on the
object that all of the external forces combined would.
Forces in two dimensions
Mass and inertia

The force vector is a way to precisely describe
the strength and direction of a force.
If you push against a block from the
horizontal, some of your force:
 accelerates the block
 pushes the block into the table

Written as x, y coordinates:
F = F(cos θ), F (sinθ)
From picture example (30.3 N, -17.5 N)
The magnitude of the force vector is the
strength of the force.
 Think of the x- and y-components of a
force vector as actual forces.
o X-force is applied along the x-axis
o Y-force is applied along the y-axis
o Total effect would be the same as
the single resultant force
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The larger the mass of an object, the
greater its inertia
o ping-pong ball
o basketball
The greater the mass of an object, the
less the object accelerates under an
applied force
Inertia of an object is proportional to
the object’s mass
Mass is a measure of the inertia of an
object
Forces and the
Laws of Motion 5
Sample Problem B
Sample #2
Derek leaves his physics book on top of a
drafting table that is inclined at a 35°
angle. The free-body diagram shows the
forces acting on the book. Find the net
force acting on the book.
An agriculture student is designing a support to
keep a tree upright. Two wires have been
attached to the tree and placed at right angles to
each other. One wire exerts a force of 30.0 N on
the tree; the other wire exerts a 40.0 N force.
Determine where to place a third wire and how
much force it should exert so that the net force
acting on the tree is equal to zero.
Step 2: select a coordinate system and
apply it to the free-body diagram.
Equilibrium: the state in which the net force
acting on an object is zero.
 Object is at rest
 Object is moving with a constant velocity
Step 3: find the x and y components of
all vectors.
If the forces act in 2 dimensions, then all of the
forces in the x-direction and y-direction
balance separately.
 the forces in the x-direction must equal 0
 the forces in the y-direction must equal 0
Step 4: find the net force in both the x
and y directions
Step 5: find the net force
A gymnast with a weight of 700 N supports
himself with 2 rings. If he is at rest (and in
equilibrium), the net force on his body is zero.
Gravity pulls down with a force of 700 N, so the
ropes must pull up with a force of 350 N each
(1/2 of his weight supported by each arm).
Forces and the
Laws of Motion 6
Section 4.3 Newton’s Second and Third Laws
Relating force, mass, and acceleration
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If the gymnast is holding himself with his
arms outstretched at 45° angles, the work is
more strenuous because only part of the
force from each arm is vertical.
The total force must be larger because the
vertical component of force in each arm
must still equal ½ his weight.
Equilibrium in the y-direction
350 N = Fy = F(sin θ)
350 N = F (sin 45°)
F = 350 N = 495 N
Sin 45
The horizontal components of force from
the left and right arms cancel each other
because they have equal magnitude and
are in opposite directions.
Sample problem C #2
An 8.5 kg bowling ball initially at rest is
dropped from the top of an 11 m building.
The ball hits the ground 1.5 s later. Find the
net force on the falling ball.
An object experiencing no net force is
in equilibrium
An object experiencing a net force
undergoes a change in its velocity
Force is proportional to mass and
acceleration
Newton’s second law of motion
The acceleration of an object is directly
proportional to the net force acting on the
object and inversely proportional to the
object’s mass.
Mathematically:
a = ΣF
m
or
F = ma
ΣF represents the vector sum of all
external forces acting on the object, or
the net force.
Sample Problem C
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
force acting on the book is 1.6 N to the
right, what is the book’s acceleration?
Forces and the
Laws of Motion 7
Newton’s 3rd law of motion
A force is exerted on an object when that object interacts with another object in its
environment.
 A single force cannot exist
 Forces always exist in pairs
 Ex. A car collides with a concrete barrier
o Car exerts a force on the barrier
o Barrier exerts a force on the car
In formal language …
If two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal
to the magnitude of the force simultaneously exerted on object 2 by object 1, and these two
forces are opposite in direction.
More clearly!
For every action, there is an equal and opposite reaction.
 Action-reaction pair
 Object 1 exerts a force on object 2 = action force
 Object 2 exerts a force on object 1 = reaction force
o Reaction force occurs at exactly the same time as the action force
Important comments on Newton’s 3rd law:
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Each force in an action-reaction pair acts on a different object
Equal and opposite forces do not balance each other and equal zero – WHY?
o Forces act on different objects
Action-reaction pairs do not imply that the net force on either object is zero
o Action-reaction forces are equal and opposite, but either object may still have
a net force acting on it.
Field forces
Why doesn’t the Earth shake?
Field forces are also affected by actionreaction pairs
 Ex. Calibration of crash-test dummies
Engineers calibrate the sensors in the
heads of crash-test dummies by dropping
the heads from a known height.
o The earth exerts a force on the
dummy
o The dummy exerts a force on the
earth
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Force of the dummy on Earth is
equal to the force of Earth on the
dummy.
The falling object accelerates
toward the earth, the earth
accelerates toward the falling
object.
Think about Newton’s 2nd law.
The mass of the Earth is so much
greater, its change in
acceleration is negligible.
Forces and the
Laws of Motion 8
Section 4: Everyday Forces
Weight
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Gravitational force exerted on an object
by Earth, Fg, is a vector quantity
Magnitude of this force, Fg, is a scalar
quantity that we call weight
Fg = mag, where ag is the acceleration
due to gravity OR
Fg = mg, where g equals the
acceleration due to gravity on the
surface of the Earth
Weight ≠ Mass
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Mass is an inherent property of an object – it does not change
Weight is not an inherent property – it changes due to the force of gravity at the
current location
o Even on Earth, objects may weigh less – the value of gravity is slightly less at
higher elevations than at sea level
o Gravity also varies slightly with changes in latitude
The Normal Force
Image your television set sitting on a table
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Force of gravity pushes down on the TV
Something pushes up on the TV because it is in equilibrium (it isn’t falling through
the table)
Force exerted on the TV by the table is the normal force, Fn
Normal is used because the direction of the contact is perpendicular to the table
surface
o The normal force always acts perpendicular to the surface, even when the
surface is at an angle to the ground
o The normal force is not always opposite in direction to gravity
Forces and the
Laws of Motion 9
Calculating normal force
In the absence of other forces, the normal force is equal and opposite to the component
of Fg that is perpendicular to the contact force.
 Normal force can be calculated as:
Fn = mg cos Θ
 The angle, Θ, is measured between the normal force and a vertical line
 The angle Θ is the angle between the contact surface and a horizontal line
Friction –force that opposes motion
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Static friction: resistive force that keeps the object from moving, Fs
o As long as the jug isn’t moving, the force of static friction is always equal to
and opposite in direction to the applied force.
o Fs = -Fapplied
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As the applied force increases, the force of the static friction also increases
When the applied force is as great as it can be without movement, the force of
the static friction has reached its maximum, Fs,max
Movement!
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When the applied force exceeds Fs,max, the object (jug, whatever) starts to move
Friction still exists, but is less than Fs,max
Kinetic friction: (Fk) frictional force on an object in motion
The magnitude of the net force acting on the object is the difference between
the applied force and kinetic friction
o Fapplied – Fk = Fnet
Forces and the
Laws of Motion 10
Looking at friction
Calculating frictional forces
All surfaces have some microscopic
irregularities on them
 Smoothest surface is obsidian (volcanic
glass)
 These irregularities stick together at
contact points (adhesion) called
microwelds
 Adhesion is caused by electrostatic
forces between the molecules of the
two surfaces
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Depicting friction in free-body diagrams
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Force of friction is always parallel to the
surface of contact
Force of kinetic friction always opposes
the direction of motion
For static friction, use the principle of
equilibrium (the frictional force points in
the direction that results in a net force of
zero)
Friction force is proportional to normal force
Which is easier to move … an empty student
desk or a heavy (full) teacher’s desk?
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The force of friction is proportional to the
magnitude of the normal
A heavier object has a heavier normal
force and therefore, greater friction!
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The force of friction depends on the
composition and qualities of the
surface in contact
o Sliding a chair across a waxed
floor is easier than sliding that
same chair across a carpeted
floor
The quantity that expresses the way
that different surface affect friction is
called the coefficient of friction (μ).
o The coefficient of friction is a
ratio of forces:
μk = Fk
Fn
o The coefficient of static friction
is the ratio of the maximum
value of static friction to the
normal force
μs = Fs,max
Fn
o If you know the value of μ and
the normal force, you can
calculate the force of friction
Ff = μFn
o See page 138 for different
coefficients of friction
Sample Problem D
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.
Forces and the
Laws of Motion 11
The inclined plane
An inclined plane is a straight surface, usually with a slope.
 The angle of the incline is the angle relative to the horizontal direction.
 When objects move along an incline, they move parallel to the surface.
A block sliding down a ramp has 3 forces acting on it:
1. gravity (weight)
2. the reaction force from the surface (normal force)
3. friction
Motion along the ramp depends on the sum of these 3 forces. Because the ramp is usually at
an angle, these 3 forces must be treated as vectors.
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Best coordinates to use for an included plane are aligned with the surface and not
with gravity
Any motion that occurs must be parallel to the surface
o Motion in the x-direction is along the surface
o No motion in the y-direction because that would mean the object is lifting off or
going through the ramp!
Resolve weight vectors in ramp coordinates
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Force of gravity on an object always acts in a direction toward the center of the Earth.
When the surface is a ramp, gravity is still straight toward the ground, but not
perpendicular to the surface of the ramp
o Resolve gravity into components parallel (x) and perpendicular (y) to the ramp
o For the angle θ, weight is represented by
Fw = mg(sin θ), mg(cos θ)
Force along the incline
A block accelerates down a ramp (in the xdirection) because its weight creates a force
parallel to the incline.
 Force parallel to the surface is
Fx = mg(sin θ)
In the y-direction, there is equilibrium (the block
isn’t falling through the ramp or lifting off of the
ramp): Fy + Fn = 0
Forces and the
Laws of Motion 12
Sample Problem E
Air resistance is a form of friction
A student attaches a rope to a 20.0 kg box
of books. He pulls with a force of 90.0 N at
an angle of 30.0° with the horizontal. The
coefficient of kinetic friction between the
box and the sidewalk is 0.500. Find the
acceleration of the box.
Whenever an object moves through a fluid
medium (gas or liquid), the fluid provides a
resistance to the object’s motion.
 Air resistance (FR) on a moving car acts
opposite to the car’s motion
 Low speeds, FR is roughly proportional
to the car’s speed
 High speeds, FR is proportional to the
square of the car’s speed
 When FR equals the car’s forward
force, net force is zero and the car
moves at constant speed
Also occurs with falling objects.
 Freely falling objects accelerate, and
velocity increases
 As velocity increases, air resistance
also increases
 When the upward force of air
resistance balances the downward
gravitational force, net force on the
object is zero
o Object then moves at a constant
maximum speed
 Terminal velocity
4 fundamental forces
All 4
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fundamental forces are field forces:
Electromagnetism
Gravitational force
Strong force
Weak force
Friction results from the interactions between the protons and electrons in atoms and
molecules.
Any force that is observed at the macroscopic level is due to electromagnetism or
gravitational force.
 Electromagnetism and gravity are field forces that act over long ranges
 Strong force and weak force both have very small ranges, so their affect is not
observable
In terms of strength:
 Strong force is the strongest
 Gravitational force is the weakest