Physics 1A
Lecture 4B
"Fig Newton: The force required to accelerate
a fig 39.37 inches per second.”
--J. Hart
Newton’s 1st law
An object continues in its state of motion at a
constant speed along a straight line, unless
compelled to change that state by a net force.
Where a net force is a vector sum of all forces on
an object (ΣF).
Note: Being at rest is a “state of motion”. A net
force is required to change that state of motion.
Forces
In order to help us understand Newton’s Laws we
will turn to the help of force diagrams (also called
free-body diagrams).
With a force diagram you represent the object
experiencing the motion as a dot and draw all the
force vectors acting on that object.
For example, for a chair sitting in the middle of a
room the force diagram would be:
Fground on chair
Fgravity on chair
chair
By Newton’s 1st Law:
ΣF=0
Inertia
Some things are harder to change the motion
of compared to others.
For example, if a baseball is thrown at you it
is rather easy to stop its motion.
But if a freight train is heading towards you
(with the same velocity as the baseball) it is
much harder to stop its motion.
Why is one harder to stop than another?
Inertia
Inertia is the natural tendency of an object to
remain at rest or in motion at a constant speed
along a straight line.
Inertia is a scalar.
Note: inertia is not a force.
Inertia is measured by the quantity of mass (kg).
Something that has a mass of 1,000kg has 1,000
times more inertia than something that has a mass
of 1kg.
Newton’s 2nd Law
When a net external force (ΣF) acts on a mass m,
an acceleration, a, will result per the following
formula:
or
The unit of net force is the Newton = (kg)(m/s2).
Newton’s Second Law of Motion basically states how an
object will accelerate based on all of the external (or
outside) forces that are upon it.
Aside on 2nd law
The second law is more correctly written as:
F = dp/dt
Here p = momentum = mv
For now, we will assume that m is constant,
and thus dp/dt = m dv/dt
We’ll get back to the more general
expression later.
Newton’s 2nd Law
Newton’s Second Law is the bridge between forces
and kinematics. An external net force will lead to
an acceleration on an object.
Please note that Newton’s Second Law is not
concerned with any one particular force, but
instead with the vector sum of ALL forces on an
object.
If I push against the wall with a force it doesn’t
necessarily accelerate the wall, this is because all
of the forces acting on the wall need to be taken
into account.
Newton’s 2nd Law
When drawing force diagrams, forces should be
properly labeled for clarity.
Ftype, object 2 on object 1
For example, a car drives in a straight line at a
constant speed. Make a force diagram for the car.
Fcontact, ground on car
Ffriction, ground on car
Fgravity, Earth on car
car
Fpush, ground on car
ΣF = 0
a=0
Newton’s 2nd Law could not be applied to any single
force on the car, only to the net force on the car.
Newton’s 2nd Law
Newton’s Second Law will also exhibit independence
in horizontal and vertical directions (like
kinematics).
Forces in the x-direction will not affect forces in
the perpendicular y-direction.
Newton’s Second Law can be broken up into
independent perpendicular directions.
In Class Question
Which one of the following statements about forces
is correct?
A) If there’s no net force on an object, the object
is at rest or will immediately come to rest.
B) An object that remains at rest could have a net
force that is non-zero.
C) An object that is continually moving must have a
net force on it.
D) In general, force is proportional to velocity.
E) All of the above statements are incorrect.
Types of Forces
There are many types of forces that we will apply
in this class, let’s discuss a few.
1) Gravitational Force:
Newton found that every body in the universe
attracts every other body in the universe given by
the equation:
where G is the universal
gravitational constant.
Gravitational Force
The direction of the force will be along the line
connecting the two masses; it will always be
attractive.
For a human on the surface of the Earth:
Gravitational Force
For a mass near the surface of the Earth:
Fgravity = mg
This force is directed downward, towards the
center of the Earth.
This is also known as weight (measured in N).
Mass and weight are different. Mass is a scalar
and will remain the same value no matter where
you are in the universe.
Weight is a vector which will change magnitude
and direction depending on where you are.
Normal Force
2) Tension Force:
When a cable or rope pulls an object, this applies a
force to the tied object known as the tension force.
3) Normal Force:
As gravity pulls down on an object, whatever that
object is resting upon will push back.
This push back is called the normal force and is
perpendicular to the surface.
The resistance of the surface to being compressed
is what leads to the normal force.
Solving Force Problems
Guidelines:
1) Choose an appropriate coordinate system. (You
may have to make a clever choice.)
2) Make a free-body diagram. (Label forces as
clearly as possible.)
3) Break force vectors into perpendicular
components. (If not already.)
4) Choose appropriate Newton’s Law to apply. (You
may need to apply more than one.)
5) Perform algebra or math techniques.
Normal Force
Example
A crane exerts an upward force of 1,000N on
a stationary 1,000kg concrete block that lies
on a pier. What is the normal force of the
pier on the concrete block?
Answer
First, you must define a coordinate system.
Let’s choose up as positive.
Normal Force
Answer
Next, we draw a free-body diagram:
Ftension, crane on block
Fnormal, ground on block
block
Fgravity, Earth on block
No need to break the forces into components, so
we can turn to Newton’s Laws.
ay = 0
ΣFy = 0
Ftension
Fnormal
Fnormal
Fnormal
+
=
=
=
Fnormal = Fgravity
Fgravity - Ftension
mg - (1,000N)
(9,800N) - (1,000N) = 8,800N
Frictional
Force
4) Frictional Force:
When an object attempts to move over a surface,
there will be a resistance known as friction.
When an object is at rest and you are attempting to
move it, the resistance is known as static friction, fs.
Static friction will increase as the applied force
increases until it reaches a maximum static friction
given by:
where μs is the coefficient of static friction and FN
is the normal force.
Frictional
Force
In general, the
static friction
can be written
as:
Frictional Force
The static force will be in the direction
opposite the applied force that is attempting
the motion.
Before you can get an object to move you
must overcome the maximum static friction.
Once you have an object moving over a
surface, the friction will become kinetic
friction, fk.
Kinetic friction is less than the maximum
static friction for a given surface.
Frictional Force
To calculate kinetic friction use:
where μk is the coefficient of kinetic friction and FN
is the normal force.
If an object moves through the air, there will be
resistance due to the air.
This resistance is called air resistance or drag.
The direction of air resistance is opposite the
direction of the velocity of the moving body.
Newton’s 3rd Law
Newton’s Third Law
“Whenever one body exerts a force on a second
body, the second body exerts an oppositely
directed force of equal magnitude on the first
body.”
This law is sometimes shortened to:
“For every action, there is an equal, but opposite
reaction.”
The third law is the one that is most often
misconstrued.
Let’s look at a game of Tug-Of-War.
In Class Question
Who wins a game of Tug-Of-War between a 80kg
person and a 60kg person?
A) A tie, Newton’s Third Law tells that neither can win,
because the force between them is equal and opposite.
B) The 80kg person, because the 80kg person will
always exert a greater force than the 60kg person.
C) The 60kg person, because the force exerted by this
much mass is greater than the 80kg person.
D) You can’t tell until you draw your force diagram for
this situation, and know more about the coefficients of
friction for both people and the surface they stand on.
Newton’s 3rd Law
Draw a force diagram for each person separately.
Fnormal, ground on 80kg
Ffriction, ground on 80kg
Fgravity, Earth on 80kg
80kg
Ftension, 60kg on 80kg
Fnormal, ground on 60kg
Ftension, 80kg on 60kg
60kg
Fgravity, Earth on 60kg
Ffriction, ground on 60kg
The winner of the tug-of-war contest is not who is
the strongest (FA on B = FB on A), but whoever had the
most friction with the ground.
For Next Time (FNT)
Start the Chapter 4 HW.
Finish Reading Chapter 4.