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Chapter 4 Dynamics
Newton’s Laws of Motion
Force: What is it?
• Force = any kind of a push or a pull on an
object.
• To exert a force = to put a push or pull on an
object.
Force: What does it do?
• If an object is at rest, it takes force to get it
moving.
• If an object is already moving, a force will
change its velocity, either in direction or
magnitude.
• In short, to accelerate an object, a force is
required.
• We can define force as an action capable of
accelerating an object.
Force as a vector
• Picture a box on the floor.
• How many ways can I make the box move?
• How many different directions can I move the
box?
• Force is a vector, it has a magnitude (how hard
I push or pull) and a direction (where I push or
pull).
Aristotle’s view
• Back in ancient Greece, Aristotle observed
that the only way to move an object was to
push or pull it.
• He argued that an object’s natural state was to
be at rest.
• He also argued the greater the force the
greater its speed.
• This idea lasted 2000 years!
Along comes Galileo
• Galileo comes around and argues that it is just
as natural for an object to be in horizontal
motion with a constant velocity.
• After 2000 years of Aristotle, Galileo must
have some powerful proof right? Some
creative experiment that disproves Aristotle or
something.
Actually…
• …Not really, all Galileo had was this:
• Imagine a heavy block pushed across a rough
surface.
• Now picture the same block pushed across a
smooth surface.
• What changes?
• Now picture a surface that does not rub
against the block at all.
Why is Aristotle Mistaken?
• We already said that to change velocity, a
force is required.
• So to slow an object down requires a force.
• The only reason you have to keep pushing an
object is to overcome the force of friction.
• More on what that means soon, but first,
introducing…
Newton’s 3 laws of motion: the 1st law
• Isaac Newton was the first scientist to actually
produce the evidence to support Galileo’s
idea.
• It was his work that resulted in 3 famous laws,
the 1st being the following:
• An object in motion stays in motion, or an
object at rest stays at rest, until acted upon by
an outside force.
Inertia
• Some objects change speed or direction easily
and some objects do not.
• The ability of an object to maintain its velocity
is called inertia.
Newton’s 2nd Law
• Everything we just covered goes into Newton’s
2nd law.
• A force will give a bigger mass less
acceleration than a smaller mass.
• This is explained in the following law:
F  ma
F  ma
•
•
•
•
ΣF means the sum of all forces
m = mass
a = acceleration
By sum of all forces I mean that multiple
forces can work with or against each other
Units of Force
• In honor of Newton, the unit of force is called
a newton, N.
• 1N is defined as the amount of push it takes to
give a 1kg object an acceleration of 1m/s2
• So 1N = 1kgm/s2
Example
• Estimate the force needed to accelerate a
1000kg at ½g and a 200-g apple at the same
rate.
Solution
• Car: m = 1000kg, a = 1/2g, which is about
5m/s2
• ΣF = ma = 1000kg x 5m/s2 = 5000kgm/s2 =
5000N
• Apple: m = 200g = 0.2kg, a = 5m/s2
• ΣF = ma = 0.2kg x 5m/s2 = 1kgm/s2 = 1N
Example
• What force is needed to bring a 1500kg car to
rest from a speed of 100km/h within a
distance of 55m?
Solution
• We will need to use ΣF = ma, but first we will
need to find the acceleration.
• So let’s look at what we got: v0 = 100km/h, v =
0km/h, x0 = 0, and x = 55m
• So we need to use, v2 = v02 + 2a(x – x0) and
solve for a,
v v
0  28m / s 
2
a

 7.1m / s
2x  x0 
255m 
2
2
0
2
Solution part 2
• Finally we can use ΣF = ma
• ΣF = ma = (1500kg)(-7.1m/s2) = -11000N or 1.1 x 104 N
Cyclops
•
•
•
•
Name: Scott Summers
Team: The X – men
Code name: Cyclops
Abilities: Can shoot
beams of “pure force”
from his eyes.
• Question: Why doesn’t
Scott’s head fly off
when he fires a beam?
Newton’s 3rd Law
• Newton’s 3rd law is this: Whenever one object
exerts a force on a second object, the second
object exerts an equal and opposite force on
the first.
• This law is also restated as “forces always
come in pairs”.
• Imagine a book on a table. Gravity pulls it
down and the table pushes it back up.
Back to Cyclops
• When Scott Summers forces a beam from his
eyes, the beam should but a force back on
Scott.
• And not just any force but an equal force in
the opposite direction.
• According to Newton, either Scott should fly
back when he fires a beam, or his head should
be ripped from his body.
Applications of Newton’s 3rd
• This law is extremely important.
• It is what let’s us walk, it makes cars go forward,
and it puts rockets into space.
• Your foot puts a force on the ground and the
ground puts an equal force back on you (friction),
which pushes you forward.
• Ditto for the car’s tires.
• In a rocket, expanding gas is pushed down out of
the rocket, the gas pushes back on the rocket
sending it up.