Download The Laws of Motion

The Laws of Motion
Newton’s Three Laws
What is a Force?
It is something we experience every single day.
You are exerting a force on your pencil right now as you
copy these notes or perhaps you are pressing down on
computer keys
Even if you think to yourself, “well I am not taking notes,”
you are still experiencing the force of gravity pulling you
down and your chair exerting a force up so…there is no
escape from the force of gravity! Well there is…but we will
get to that in another lecture…
Newton’s First Law
If an object does not interact with any other objects, it
is possible to identify a reference frame in which the
object has zero acceleration
This is called an “inertial reference frame”
All inertial reference frames can be related to each
other by constant velocities
Inertial reference frames DO NOT accelerate relative
to each other
Be careful: not all reference frames are inertial!
Newton’s First Law (cont.)
In terms of a reference frame, imagine you have an air
hockey table inside a train moving 20 m/s relative to
the ground. A hockey puck on the table, experiencing
almost no friction, appears to not be moving but we
know the train is moving so the puck must also be
moving at 20 m/s relative to the ground.
Both velocities for the air hockey puck are correct in
their respective reference frames…
Newton’s First Law (cont.)
If the train were to speed up or slow down, the puck
would then begin to move and maintain its 20 m/s
speed because there is no friction between it and the
table and nothing to act on it to change its velocity
So the first law can be stated: A body at rest or at
constant velocity in the absence of an external force
will remain at rest or at constant velocity
In other words, when no force acts on an object, the
acceleration of the object is zero
Newton’s Second Law
But what happens to an object when a force acts on it?
Imagine exerting a force on the air hockey puck and
pushing it across the frictionless surface. The block
must have experienced a change in velocity (i.e. an
acceleration) if it went from stationary to moving. The
more force you apply, the more the block will
accelerate
There is a direct relationship between force and
acceleration
Newton’s Second Law (cont.)
What else affects the acceleration?
Would a larger block accelerate as quickly with the
same amount of force it took to move the first one?
The answer is no – it would take more force to move
the larger block at the same acceleration
So there is an inverse relationship between acceleration
and a property of the object called its “mass”. Mass is a
measurement of an object’s resistance to acceleration!
Newton’s Second Law (cont.)
When viewed from an inertial reference frame, the
acceleration of an object is directly proportional to the
net force acting on it and inversely proportional to it’s
mass
This is represented by the formula:
This is in general a VECTOR equation; both force and
acceleration are vectors! The total acceleration (if there are
multiple forces) can be found as a vector sum.
Newton’s Second Law (cont.)
A simple example:
If a block had a mass of 10 kg and the force you
applied accelerated it by 10 m/s2, what is the
magnitude of the force?
How much force would you need to apply to a larger
block that had a mass of 50 kg in order to achieve the
same acceleration?
What are the units of these forces?
Newton’s Third Law
The Law of Action and Reaction
If two objects interact, the force exerted by object 1 on
object 2 is equal in magnitude and opposite in direction
to the force exerted by object 2 on object 1
If they were added together, the sum of those two forces
is zero because they are equal in magnitude and opposite
in direction (which would mean they cancel each other
out)
So, if every force produces an equal and opposite
reaction force, how does anything ever move?
Newton’s Third Law (cont.)
Imagine book sitting on a table. It is not moving
because the table is exerting a force up equal the
amount of force down that the earth is pulling on the
book. But this force the table is exerting is not the
reaction force Newton’s Second Law is talking about.
The reaction force is that the book is also pulling on
the earth with the same amount of force that the earth
is pulling on the book – the is the true equal and
opposite reaction force! Notice that the reaction force
ALWAYS ACTS ON A DIFFERENT OBJECT!
Review
First Law: A body at rest tends to stay at rest unless
acted on by an external force and an object in motion
tends to stay in motion unless acted on by an external
force
Second Law: The acceleration of an object is directly
proportional to vector sum of the forces acting on it
and inversely proportional to its mass
Third Law: For every action there is an equal and
opposite reaction