Download Second Law teacher power point

Newton’s Second
Law
How the apple fell from the tree…
The second Law
F= m x a
History

Isaac Newton was one of the world’s great
scientists. He combined his ideas and the
ideas of earlier scientists, such as Galileo,
into a unified picture of how the universe
works.

Isaac Newton explained the workings of
the universe through mathematics. He
formulated laws of motion and gravitation.
These laws are math formulas that explain
how objects move when a force acts on
them. Principia, his most famous book,
explained three basic laws that govern the
way objects move. These three laws are
known as Newton’s Laws.
http://cascooscuro.files.wordpress.com/2007/08/sir_isaac_newton_1643-1727.jpg
What is a force?
A force is a push or a pull on
any object with a mass.
The second law States that the
sum of all the forces pushing
or pulling the object is directly
proportional to how fast the
object is speeding up.
History



Newton’s First law of Motion
I. Every object in a state of uniform motion tends to
remain in that state of motion unless an external force
is applied to it.
Newton's Second Law of Motion:
II. The relationship between an object's mass m, its
acceleration a, and the applied force F is F = ma.
Acceleration and force are vectors (as indicated by their
symbols being displayed in slant bold font); in this law the
direction of the force vector is the same as the direction
of the acceleration vector.
Newton's Third Law of Motion:
III. For every action there is an equal and opposite
reaction.
What is a Force?

If an object is
speeding up at
a constant rate,
then a force is
being exerted
on the object.
http://www.mirage-replicas.co.uk/img/Race.jpg
What is the net force?
This is the most powerful of Newton's three
Laws, because it allows us to calculate how
objects move: It allows us to relate what
moves to why it moves.
It also answers how and why speeds change
when forces are applied
How do we measure Force?

Forces are measured using the units of
mass and acceleration combined. The SI
standard unit of force is the Newton, N. In
America, the standard unit of measure of
weight is pounds, or lbs.
Weight


Weight is a force acting
down on a mass
Your weight is the force
that the earth exerts on
you to keep you on the
ground. The Earth
exerts gravity that pulls
you down.
http://www.3dnworld.com/users/1/images/UltimateEarth.jpg
Example

10 kg
If an object has a mass of 10 kg and you
push on the object so that it speeds up
uniformly at 10 meters per second every
second the Force exerted on the object
would be:
(10 kg) x (10 m/s2) = 100 Newtons

If a rope attached to an object pulls with
a force of 24 newtons and the mass of
the object is 6 kg, how fast is the object
speeding up?
24 N = (6kg) x acceleration
24 / 6 = acceleration = 4 m/s2
6 Kg
Atwood’s Machine
Atwood’s machine
is a simple
machine allows
us to calculate
gravity and mass.
Concept of Atwood’s Machine
Greater weights will
cause the machine
to accelerate in the
direction of that
weight.
What forces are
acting on each
individual mass?
Gravity is the only
force “pulling” on
the lager mass.
Tension in
rope
For the smaller mass,
gravity pulls down
and the rope pulls
up.
Weight of smaller
mass
Weight of
larger mass
Concept of Atwood’s Machine
The system
accelerates in the
direction with the
heaviest weight. Is
this in concord with
the laws of gravity
and balance?
1 kg
2 kg
What about friction?
Friction is defined as the resistant force between two objects’
nonsmooth surfaces
It always acts against an object.
What about friction?

Imagine a wooden brick tied to a weight on
a horizontal table. If the weight is hung over
the edge of the table, the wooden brick will
accelerate in the direction the string is
being pulled (horizontally).
String
Block
Table
What about friction?
In this scenereo, gravity is not the only
force acting on the block-weight system.
Friction is also exerting a force opposite
that of gravity.
String
Friction
Block
Table
Weight exerted by gravity
What about friction?

That means that friction is acting against
the pull of the string and the direction of the
motion.

What can you conclude about the
relationship between gravity and the net
acceleration by adding in friction?
Practice Problems

Try some problems on your own:
Practice Problems

An apple that has a mass of
2 kg falls with a net
acceleration of 2m/s2 from
the largest tree in the world.
Air resistance also acts on
the apple. What is the total
force acting on the apple?
How does this compare to
the apple’s weight on the
ground? What if there was
no air resistance?
Practice answers

We can set up our equation using what we
know from Newton’s second law
Force = mass x acceleration
So:
Force = (2kg) x (2m/s2)
Force = 4N
Practice answers

The weight of the object on the ground is:
(mass) x (gravity)
This is equal to:
(2kg) x (9.81 m/s2)
We can conclude that the apple’s weight is
greater than the force acting on the apple in
the air
Practice answers

If there was no air resistance, the apple
would fall with an acceleration of gravity,
9.81 m/s2, and the force acting on the apple
in the air would be equal to that of the
apple’s weight on the ground.
Practice Problems

Two monster dogs pull on an 80 kg rope.
Monster dog #1, Pepe, pulls to the left with
a force of 12 N. Jumbo, monster dog # 2,
pulls to the right with a force of 6 N. How
fast is the rope speeding up and in what
direction?
Practice answers
First we must find the direction of each force.
One dog pulls to the left, the other dog pulls
to the right.
Pepe
Jumbo
Practice answers

Both dogs pull in opposite directs so the
total force is the result of one force
subtracted from the other
Practice answers

We can then set up our equation:
Force = 12N - 6N = mass x acceleration
+
_
12N
6N
Practice answers

We know the mass of the rope is 80 kg, so:
12N - 6N = (80kg) x a
6N = (80kg) x a
a=0.075 m/s2
_
+
6N
12N
80 kg
Questions and Discussion
References

http://csep10.phys.utk.edu/astr161/lect/hist
ory/newton3laws.html
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http://en.wikipedia.org/wiki/Image:Atwoodm
achine.gif
http://www.dictionary.com
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