2-Dimensional Motion
&
Newton Laws of Motion
(sections 5.1-5.4)
Kinematics: Assumptions,
Definitions and Logical Conclusions
What have we done so far?
• Defined displacement, velocity, acceleration (also
position, distance, speed)...
• Defined scalers (like speed) and vectors (like velocity)
• Laid out assumptions about free-fall
• noticed that 2-dimensional motion is really just two,
simultaneous, 1-dimensional motions.
Used this to shoot a monkey, range out a
small cannon, etc.
This wasn’t physics. This was preparing the language
needed to talk about physics.
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Newton’s Laws
How can we consistently and
generally describe the way
objects move and interact?
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Isaac Newton
1643-1727
1702 portrait
Newton in a 1689
by Godfrey Kneller
Nature and nature's laws lay hid in night;
God said "Let Newton be" and all was light.
Newton’s epitaph, Alexander Pope
I do not know what I may appear to the world, but to myself I
seem to have been only like a boy playing on the sea-shore,
and diverting myself in now and then finding a smoother
pebble or a prettier shell than ordinary, whilst the great ocean
of truth lay all undiscovered before me.
from a memoir by Newton
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Force
Force: push or pull
Force is a vector – it has magnitude and
direction
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Mass
Mass is the measure of
how hard it is to change
an object’s velocity.
Mass can also be thought
of as a measure of the
quantity of matter in an
object.
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Newton’s First Law of Motion
If you stop pushing an object, does it stop
moving?
Only if there is friction!
In the absence of any net external force, an object at rest
will remain at rest.
In the absence of any net external force a moving object
will keep moving at a constant speed in a straight line.
This is also known as the Law of Inertia.
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Inertia
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Newton’s First Law
A hockey puck
slides on ice at
constant
velocity. What is
the net force
acting on the
puck?
a) more than its weight
b) equal to its weight
c) less than its weight but more than zero
d) depends on the speed of the puck
e) zero
Newton’s First Law
A hockey puck
slides on ice at
constant velocity.
What is the net
force acting on
the puck?
a) more than its weight
b) equal to its weight
c) less than its weight but more than zero
d) depends on the speed of the puck
e) zero
The puck is moving at a constant velocity, and
therefore it is not accelerating. Thus, there must
be no net force acting on the puck.
Follow-up: Are there any forces acting on the puck? What are they?
Newton’s First Law
You put your book on
a) a net force acted on it
the bus seat next to
b) no, or insufficient, net force acted on it
you. When the bus
c) it remained at rest
stops suddenly, the
book slides forward off
the seat. Why?
d) it did not move, but only seemed to
e) gravity briefly stopped acting on it
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Newton’s First Law
You put your book on
a) a net force acted on it
the bus seat next to
b) no, or insufficient, net force acted on it
you. When the bus
c) it remained at rest
stops suddenly, the
book slides forward off
the seat. Why?
d) it did not move, but only seemed to
e) gravity briefly stopped acting on it
The book was initially moving forward (because it was
on a moving bus). When the bus stopped, the book
continued moving forward, which was its initial state of
motion, and therefore it slid forward off the seat.
Calibrating force
Two equal weights exert twice the force of one; this
can be used for calibration of a spring:
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Experiment: Acceleration vs Force
Now that we have a calibrated spring, we can do
more experiments.
Acceleration is proportional to force:
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Experiment: Acceleration vs Mass
Acceleration is inversely
proportional to mass:
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Newton’s Second Law of Motion
Acceleration is proportional to force:
Acceleration is inversely proportional to
mass:
Combining these two observations gives
Or, more familiarly,
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Newton’s Second Law of Motion
An object may have several forces acting on it;
the acceleration is due to the net force:
SI unit for force Newton is defined using this equation as:
1 N is the force required to give a mass of 1 kg an
acceleration of 1 m/s2
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Units of force: Newtons
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Force of Gravity
The weight of an object is the force acting on it due to gravity
Weight: W = Fg = ma = mg vertically downwards
Weight is not mass!
Since
, the weight of an object in Newtons is
approximately 10 x its mass in kg
adult human
70 kg
700 N ~ 160 lbs.
There is no “conversion” from kg to pounds!
(Unless you specify what planet you are assuming)
Newton’s First and Second Laws
(I)
In order to change the velocity of an object –
magnitude or direction – a net force is required.
(II)
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Inertial Reference Frames
(I)
In order to change the velocity of an object –
magnitude or direction – a net force is required.
(II)
Newton’s First and Second Laws do not work
in an accelerating frame of reference
An inertial reference frame is one in which the first
and second laws are true. Accelerating reference
frames are not inertial.
Is the earth an inertial reference frame?
No, but acceleration due to earth’s rotation around
Its axis (0.034 m/s2), and due to earth’s rotation around sun
(smaller) are negligible compared to g; so approximately yes.
Analyzing the forces in a system
Free-body diagrams:
A free-body diagram shows every force acting on
an object.
• Sketch the forces
• Isolate the object of interest
• Choose a convenient coordinate system
• Resolve the forces into components
• Apply Newton’s second law to each coordinate
direction
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Free-body Diagram
Example of a free-body diagram:
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Newton’s First Law
A book is lying at
rest on a table.
The book will
a) there is a net force but the book has too
much inertia
b) there are no forces acting on it at all
c) it does move, but too slowly to be seen
remain there at
d) there is no net force on the book
rest because:
e) there is a net force, but the book is too
heavy to move
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Newton’s First Law
A book is lying at
rest on a table.
The book will
a) there is a net force but the book has too
much inertia
b) there are no forces acting on it at all
c) it does move, but too slowly to be seen
remain there at
d) there is no net force on the book
rest because:
e) there is a net force, but the book is too
heavy to move
There are forces acting on the book, but the
only forces acting are in the y-direction. Gravity
acts downward, but the table exerts an upward
force that is equally strong, so the two forces
cancel, leaving no net force.
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Newton’s Third Law of Motion
Forces always come in pairs, acting on different
objects:
If object 1 exerts a force
on object 2, then
object 2 exerts a force –
on object 1.
These forces are called action-reaction pairs.
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Some action-reaction pairs
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Action-reaction pair?
a) Yes
b) No
Newton’s 3rd: F12 = - F21
action-reaction pairs are equal and
opposite, but they act on different bodies
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Newton’s Third Law of Motion
Although the forces are the same, the
accelerations will not be unless the objects
have the same mass.
Q: When skydiving,
do you exert a force
on the
earth? Does the
earth accelerate
towards you?
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Newton’s Third Law of Motion
Contact forces:
The force exerted by
one box on the other is
different depending on
which one you push.
Assume the mass of the two objects
scales with size, and the forces
pictured are the same. In which case
is the magnitude of the force of box 1
on box 2 larger?
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Truck on Frozen Lake
A very large truck sits on a
frozen lake. Assume there
is no friction between the
tires and the ice. A fly
suddenly smashes against
the front window. What
will happen to the truck?
a) it is too heavy, so it just sits there
b) it moves backward at constant
speed
c) it accelerates backward
d) it moves forward at constant speed
e) it accelerates forward
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Truck on Frozen Lake
A very large truck sits on a
frozen lake. Assume there
is no friction between the
tires and the ice. A fly
suddenly smashes against
the front window. What
will happen to the truck?
a) it is too heavy, so it just sits there
b) it moves backward at constant speed
c) it continuously accelerates backward
d) it moves forward at constant speed
e) it continuously accelerates forward
When the fly hit the truck, it exerted a force on the truck
(only for a fraction of a second). So, in this time period,
the truck accelerated (backward) up to some speed. After
the fly was squashed, it no longer exerted a force, and
the truck simply continued moving at constant speed.
Follow-up: What if the fly takes off, with the same speed in the
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direction from whence it came?
A 71-kg parent and a 19-kg child meet at the center of an ice rink. They
place their hands together and push.
(a) Is the force experienced by the child more than, less than, or the
same as the force experienced by the parent?
(b) Is the acceleration of the child more than, less than, or the same as
the acceleration of the parent? Explain.
(c) If the acceleration of the child is 2.6 m/s2 in magnitude, what is the
magnitude of the parent’s acceleration?
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On vacation, your 1300-kg car pulls a 540-kg trailer away from a
stoplight with an acceleration of 1.9 m/s2
(a) What is the net force exerted by the car on the trailer?
(b) What force does the trailer exert on the car?
(c) What is the net force acting on the car?
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