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Unit Two: Dynamics
Section 1: Forces
Look in glossary of book …
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What is the difference between dynamics and
kinematics?
What is a force? What can a force do? What
causes a force?
Key Terms:
Dynamics
Kinematics
Force
Gravitational Force
Strong Nuclear Force
Inertia
Net Force
Normal Force
Weight
Mass
What is dynamics???
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Kinematics: The study of how objects
move (velocity, acceleration)
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Galileo performed experiments that allowed him
to describe motion but not explain motion.
Dynamics: The study of why objects
move.
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The connection between acceleration and its
cause can be summarized by Newton’s 3 Laws of
Motion (published in 1687)
The cause of acceleration is FORCE.
Forces
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What is a force?
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Some forces cause acceleration
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A push or a pull
Example: gravity
Some forces cause stretching, bending,
squeezing
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Example: spring force
Force
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Symbol: F
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Formula: F=ma
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Force = mass x acceleration
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Units: kg x m/s2 = Newtons (N)
The 2 Main Types of Forces
Contact Forces: are forces that result when
two objects are physically in contact with one another
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Example: push/pull, normal force, friction, spring
force, tension, air resistance
Non-contact Forces: forces that result when two
objects are not in physical contact
Example: gravitational force, nuclear force, magnetic
force, electrostatic force (electric charge)
Gravitational Forces
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Example: Consider the following information
and then compare the gravitational force on
the SAME OBJECT in each case.
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A man standing near the equator (distance from
Earth’s centre = 6378 km)
A man standing near the North pole (distance
from Earth’s centre = 6357 km)
A man standing in the International Space Station
(distance = 6628 km)
A man in a space ship past Pluto
Gravitational Forces
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Gravitational force decreases as we increase
how far we are from the centre of the Earth
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It is a non-contact force
Weight Vs. Mass
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Weight and mass are NOT THE SAME.
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Weight = the force of gravity acting on a mass.
Weight can change. It is measured in Newtons
(force).
 Weight = mass x gravitational force
 Fg = mg
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Mass = the quantity of matter an object contains.
Mass for the same object is constant. It is
measured in kg.
Weight Can Change…
Examples of Weight Problems
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Mrs. Evans’ dog Pi has a mass of 17kg.
What would Pi’s weight be:
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A) On Earth?
B) On Jupiter (where g = 25.9 m/s2)
C) On the Moon (where g = 1.64 m/s2)
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Examples of Weight Problems
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A student standing on a scientific spring scale
on Earth finds that he weighs 825N. Find his
mass.
Practice
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Page 137, #1, 2, 3, 4
Normal Force
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A force that acts in a direction perpendicular
to the common contact surface between two
objects
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Example Diagram:
Friction
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A contact force
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Electromagnetic Force (between surface
atoms of objects touching)
Friction
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There are 2 types of friction:
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Static Frictional Force
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When you start to move an object from rest
Larger than Kinetic Frictional Force due to Inertia
ųs
Kinetic Frictional Force
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Exists when the object is moving
ųK
Friction
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The strength of friction depends on…
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Surface materials
Magnitude of forces pressing surfaces together
The strength of friction DOES NOT depend
on…
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Surface area
Velocity of object moving
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See page 140, table 4.5 for a list!
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Coefficient of Friction
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“Stickiness value”
Gives the maximum value of friction.
ų (symbol mu)
ų has no units
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Page 140, table 4.5
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Formula: Ff = ųFN
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Remember: FN = - Fg
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Friction Example
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During the winter, owners of pickup trucks
often place sandbags in the rear of their
vehicles. Calculate the increased static force
of friction between the rubber tires and wet
concrete resulting from the addition of 200.
kg of sandbags in the back of the truck.
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Use the table of coefficients of friction on
page 140.
Friction Example 2
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A horizontal force of 85N is required to pull a
child in a sled at constant speed over dry
snow to overcome the force of friction. The
child and sled have a combined mass of 52
kg. Calculate the coefficient of kinetic friction
between the sled and the snow.
Practice Friction Problems
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Page 144
Questions 5, 6, 7, 8
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Weight Problems
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Page 137, #1, 2, 3, 4
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Free Body Diagrams
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We usually use a box or small
circle to represent the object.
The size of the arrow is
reflective of the magnitude
(SIZE) of the force.
The direction of the arrow
reveals the direction in which
the force acts.
Each force arrow in the diagram
is labelled to indicate the type
of force.
Use math symbols to show
equality if needed.
What can you tell about these
forces??? What else could we
add?
Free Body Diagrams
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A free body diagram will be
used in most dynamics
problems in order to simplify
the situation
In a FBD, the object is
reduced to a point and
forces are drawn starting
from the point
FN
Fa
Ff
Fg
Free Body Diagram Examples
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1. A book is at rest on a table top. Diagram
the forces acting on the book.
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Refer to sheet in class with 10 examples!
Newton’s First Law of Motion
- Newton’s Law of Inertia
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An object at rest or in uniform motion (i.e.,
constant velocity) will remain at rest or in
uniform motion unless acted on by an external
force.
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Section 5.1 in text (pages 154 to 159)
Reworded: An object at rest will remain at rest until
a force is applied. An object moving at a constant
velocity will continue to move at a constant velocity if
no force is applied (ie, no acceleration).
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Inertia
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the natural tendency of an object to remain in
its current state of motion (either moving or at
rest)
Where did this come from?
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Galileo performed many experiments and
speculated that if a perfectly smooth object
were on a perfectly smooth horizontal surface
it would travel forever in a straight line.
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Newton developed this idea.
Newton’s First Law Example
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If an apple is sitting on Mrs. Evans’ desk, it
will remain there until the desk is removed
(so the normal force is removed and gravity
acts on it without an opposing force) or
someone lifts it up (applied force).
If a car is driving along a straight road at
100km/h, it will continue to do so (given the
car still has gas!) until the brakes are applied
(applied force), there is a turn/hill or the road
surface changes (more or less friction).
Net Force
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The sum of all vector forces acting on an
object.
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Example: What are the forces acting on a
stopped car? Draw a labeled diagram.
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Example: What are the forces acting on a
car moving at 100km/h [N]?
Quick Experiment
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Materials – cup, card, penny or coin
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What to do:
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Set up the card on top of the cup and the
penny on the card in the middle.
Flick the card. What happens to the card?
The penny? Why?
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Questions
1. To which object was a force applied by the flick and
which object was not acted upon by the flick?
 2. Why did the penny fall into the cup and not fly off
with the card?
 3. What force held the penny in place while the card
was flicked out? What force brought the penny down
into the cup?
 4. Would the penny move in the same way if
sandpaper was used instead of the card?
 5. Apply this learning to the reason we wear seat
belts. Why do you think babies need carseats
rather than just seatbelts?
Summary
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The inertia of every object resists the change in
motion. In this case, the inertia of the penny held it
in place while the card was flicked out from under it
(normal force was opposing the gravitational force).
The force acting on the card was not applied to the
penny. After the card was moved from under the
coin, gravity supplied the force to bring the penny
down into the cup. If a force had been applied to
both the card and the penny, then both would have
moved and the penny would not have fallen into the
cup.
Check Your Learning
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1. Why does a package on the seat of a bus
slide backward when the bus accelerates
quickly from rest? Why does it slide forward
when the driver applies the brakes?
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Use as many physics terms as possible and
describe in detail.
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The bus is initially at rest, as is the package. In the absence of any
force, the natural state of the package is to remain at rest. When the
bus pulls forward, the package remains at rest because of its inertia
(until the back of the seat applies a forward force to make it move
with the bus). NOT ENOUGH FRICTION with the seats!
From the point of view of someone on the bus, it appears that the
package is moving backward; however, someone watching from
outside the bus would see the bus move forward and the package
trying to stay in its original position.
Once the package is moving with the bus, its inertia has now
changed. It now has a natural tendency to be moving forward with a
constant speed. When the bus slows down, the package continues
to move forward with the same constant speed that it had until some
force stops it.
Force
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Symbol: F
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Formula: F=ma
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Force = mass x acceleration
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Units: kg x m/s2 = Newtons (N)
The Net Force
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The net force is a vector sum which means
that both the magnitude and direction of the
forces must be considered
In most situations we consider in Physics 11,
the forces will be parallel (ie, up and down,
etc) and perpendicular
The Net Force
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In most situations, there is more than one
force acting on an object at any given time
When we draw the FBD we should label all
forces that are acting on an object and also
determine which would cancel each other out
Ones that do not completely cancel out will
be used to determine the net force
Find the net force on each FBD
Find the net force on the FBD
FBD and Net Force Mini
Worksheet
Newton’s Second Law
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Newton’s first law states that an object does not
accelerate unless a net force is applied to the
object.
But how much will an object accelerate when there
is a net force?
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The larger the force the larger the acceleration.
Therefore acceleration is directly proportional to mass.
Acceleration also depends on mass.
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The larger the mass, the smaller the acceleration.
Therefore acceleration is inversely proportional to mass.
We say that a massive body has more INERTIA than a less
massive body.
Newton’s Second Law
- Newton’s Law of Motion
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Force = mass x acceleration
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Fnet = ma
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The acceleration is in the same direction as
the force.
Newton’s Second Law
Examples
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Ex. 1: What net force is required to
accelerate a 1500. kg race car at +3.00m/s2?
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Draw a FBD to show the net force.
Practice Problems
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Page 163, Questions 1, 2, 3
Free Body Diagrams and Fnet
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Example 1: Calculating Fnet
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I want to push my tarantula’s 8.7kg cage
across the table. I push with 29N of force,
and there is a force due to friction of 8N
between the table and the cage. What is
Fnet? Determine how much the cage will
accelerate. Draw an FBD.
Free Body Diagrams and Fnet
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Example 2: Calculating acceleration
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A man is riding in an elevator. The mass of the man
and elevator is 700. kg. What is the elevator’s
acceleration if the tension in the cable is 7500 N?
Draw an FBD.
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Describe the motion of the elevator (direction,
slowing down or speeding up).
Force-Mass-Acceleration
Relationships
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Work on sheet
Putting it All Together
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Now that we have considered Newton’s
Second Law, you can use that to analyze
kinematics problems with less information
than we have used previously
We can either use dynamics information to
then apply to a kinematic situation or vice
versa
Newton’s Second Law
Examples
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Ex. 1: An artillery shell has a mass of 55 kg.
The shell is fired from a gun leaving the
barrel with a velocity of +770 m/s. The gun
barrel is 1.5m long. Assume that the force,
and the acceleration, of the shell is constant
while the shell is in the gun barrel. What is
the force on the shell while it is in the gun
barrel?
Practice Problems
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Page 168, questions 4 to 8
Example 2
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A 25kg crate is slid from rest across a floor
with an applied force 72N applied force. If
the coefficient of static friction is 0.27,
determine:
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The free body diagram. Include as many of the
forces (including numbers) as possible.
The acceleration of the crate.
The time it would take to slide the crate 5.0m
across the floor.
FBD
FN=250N
Fa=72N
Ff=?
Fg=-250N
Use the frictional force equation to
determine the magnitude of the
frictional force
F f  FN
F f  (.27)( 250 N )
F f  66 N
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F f  66 N
The net force is the sum of the forces
(acting parallel or anti-parallel)
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Fnet
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Fnet
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Fnet
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Fnet
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  Fi
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 F f  Fa
 66 N  72 N
 5.8 N
Use Newton’s Second Law to solve
for the acceleration
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Fnet  ma
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5.8 N  (25kg)a
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2
a  0.23m / s
Use kinematics to solve for the time
taken to cross the floor
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2
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at
d (t ) 
 v0t  d 0
2
2 2
0.23m / s t
5 .0 m 
2
2(5.0m)
t
2
0.23m / s
t  6 .6 s
Tug of War
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Sometimes we have more than 1 force acting
on an object (like in a tug of war).
What are the forces at work in a tug of war?
What direction are the forces?
If your team wins, what does that mean about
the forces?
If your team loses, what does that mean
about the forces?
What other forces are there on the players?
Example 3
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A baby carriage with a mass of 50. kg is
being pushed along a rough sidewalk with
an applied horizontal force of 200. N and it
has a constant velocity of 3.0 m/s.
A) What other horizontal force is acting on
the carriage and what is the magnitude and
direction of that force?
B) What value of applied horizontal force
would be required to accelerate the carriage
from rest to 7.0 m/s in 2.0 s?
Example 3
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A) Force of friction must be equal in
magnitude (so 200.N) in the opposite
direction to the force applied (of the baby
carriage moving forward).
B) First find a using a = (vf – vi)/t = 2.0m/s2
Now find Fnet = ma = 50x2 = 100N
Now use Fnet = Fapp – Ff
Fapp = 300N = 3.0 x 102 N
Example 4
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A horizontal force of 50. N is required to pull
an 8.0 kg block of aluminum at a uniform
velocity across a horizontal wooden desk.
What is the coefficient of kinetic friction?
Example 4
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You know that Force of friction is equal and
opposite to Force applied. Therefore, Ff =
50.N.
You know that Force of friction = coefficient of
friction x normal force.
Normal Force = - Force of gravity = -mg
Fn = 78.48N
Sub in and rearrange to find that coefficient =
0.64 (no units)
Example 5
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A 75 kg man stands in an elevator. Draw a free body
diagram and determine what the force the elevator
exerts on him will be when
A) the elevator is at rest
B) the elevator is moving upward with a uniform
acceleration of 2.0 m/s2
C) the elevator is moving downward with a uniform
velocity of 2.0 m/s
D) the elevator is moving downward with a uniform
acceleration of 2.0 m/s2
Example 5
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A)
B)
C)
D)
Fnet = 0N, Fapp = 0N
Fnet = 150N [up]
Fnet = 0N
Fnet = 150N [down]
Practice Problems
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Page 170
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9, 10 and 13
System of Masses
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When two or more masses are attached by a string
or rope and hang over a pulley system, there is a
system of masses.
Some assumptions that must be made:
- Strings only exert pulling forces.
- The tension in the string is the same throughout its
length.
- A frictionless pulley changes the direction of a
string without diminishing its tension.
- Strings do not stretch.
- The strings’ mass is negligible.
Tension
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Tension is the magnitude of the pulling
force exerted by a string, cable, chain, or
similar object on another object.
It is measured in Newtons
It is measured parallel to the string on which
it applies
Example 1
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A 2.0 kg mass, placed on a smooth, level
table is attached by a light string passing over
a frictionless pulley to a 5.0 kg mass hanging
freely over the edge of a table.
A) Draw a free body diagram of the masses
B) Calculate the tension in the string
C) Calculate the acceleration of the 2.0 kg
mass
Answer
Answer continued
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The masses move together – so the
accelerations are the same!
The forces are slightly different. How?
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Ask yourself how the system will move:
First, we know that mass m is falling and
dragging mass M off the table. The force of
kinetic friction opposes the motion of mass M.
However, we know that friction is negligible
here because it is a smooth surface!
We also know, since both masses are
connected by a nonstretching rope, that the
two masses must have the same speed and
the same acceleration.
Example 2
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Two spheres of masses 1.5 kg and 3.0 kg are
tied together by a light string looped over a
frictionless pulley. They are allowed to hang
freely. What will be the acceleration of each
mass?

http://schools.hwdsb.on.ca/highland/files/201
1/01/System-of-Connected-Masses.pdf\
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Systems of Masses Worksheet
Newton’s Third Law
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When one object exerts a force on a second object,
the second object exerts a force on the first that is
equal in magnitude but opposite in direction.
These forces are called action-reaction forces.
Ex: If you push against a wall, you don’t go through
it as the wall “pushes back”.
Only the forces on an object determine its
acceleration.
Newton’s Third Law
• With equal and opposite forces, how does
anything ever move?
 Example: Picking up a ball:
Ball exerts an equal force on your hand, but
this is not on the ball and does not appear in
the free body diagram
Example
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Suppose you are floating around in space
(many km from any planet so that you feel no
gravity) outside of your spaceship. You get
frustrated and decide to kick your spaceship.
Does your foot hurt?
Solution
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Yes, your foot will hurt. Even though there is
no gravity, Newton’s Third law still applies. If
you kick the spaceship, it applies an equal
and opposite force on your foot.
Newton’s Third Law Worksheet
Inertial Frame of Reference
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A frame of reference that is at rest or moving
at a constant velocity.
Example: You moving in a car on cruise
control.
Example: You sitting at your desk.
Newton’s Laws of Motion are valid here!
Non-inertial Frame of
Reference
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An accelerating frame of reference
Example: When you suddenly stop in a car.
Example: When you are speeding up and
passing a car.
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Newton’s Laws of Motion do not apply!
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Read pages…
Frames of Reference
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Imagine you are driving in a car. Does it feel
like you have moved?
If you are watching from the road, how does
your frame of reference change?
What type of frame of
reference???
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You are standing in an elevator waiting for it
to go up 10 flights.

You are standing in an elevator that is just
starting to move.

You are standing in an elevator going down at
a constant speed.

There are two kinds of mass.
1. Inertial mass: the ratio of the net force
exerted on the object and its acceleration.
2. Gravitational mass: the comparison of
gravitational forces of two masses (one with a
known mass, the other with an unknown
mass)