- Good morning.
Today we're going to review the dynamics portion
of the AP Physics C Mechanics Curriculum.
You know, Newtons three laws and friction and stuff.
- Don't say, "And stuff," just say,
"Newton's laws and friction."
♫ Flipping Physics
- Billy, what is Newton's First Law?
- When viewed from an inertial reference frame,
an object at rest will remain at rest
and an object in motion will remain at a constant velocity
unless acted upon by a net external force.
- An inertial reference frame is
where the frame of reference has an acceleration of zero.
For example, right now, my acceleration is zero,
so this is an inertial frame of reference.
A non-inertial reference frame is where the acceleration
of the frame of reference is not equal to zero.
For example, in a car, which is turning,
which is a non-inertial reference frame,
objects which are at rest on the dashboard will,
from the frame of reference of the vehicle,
not remain at rest.
Newton's first law is also called
the Law of Inertia.
And inertia is the tendency of an object
to resist a change in state of motion
or to resist acceleration.
Bobby, what is Newton's second law?
- Newton's second law is an equation,
a net force equals mass times acceleration,
and remember force and acceleration are both vectors.
- Yes, that is the form of Newton's second law
which I prefer, but you should be aware
that has been rearranged on the AP equation sheet
to solve for acceleration.
Bo, what is Newton's third law?
- Newton's third law is also an equation.
For every force object one exerts on object two,
object two exerts an equal but opposite force on object one,
and force is, of course, a vector.
- Billy, what are the units for force?
- Force is in newtons, and newtons are,
oh, oh, net force equals mass times acceleration.
so a newton is a kilogram times a meter per second squared.
- Bobby, name and describe one
of the basic forces in dynamics, please.
- Okay, uh,
the Force of Gravity, the symbol is F sub g,
and it equals mass times acceleration due to gravity.
It is caused by the interaction between the object
and the planet, it is always down.
Here near the surface of planet earth,
the acceleration due to gravity is considered to be
a constant positive 9.81 meters per second squared.
It is synonymous with weight, so sometimes you will see
the symbol capital W used for weight or Force of Gravity
and it acts on the center of mass of the object.
- Actually, it acts on the center of gravity of the object.
- We live in a constant gravitational field,
so the center of gravity and center of mass of an object
are in the same place.
- Sure.
- Bo, another force please.
- The Force Normal F sub N.
It is a pushing force caused by a surface.
It is normal to or perpendicular to the surface.
The Force Normal is always a push,
and it acts on the contact point between the two surfaces.
- Billy, how about another force?
- Another Force of Tension, capital F
with a subscript of capital T,
the Force of Tension is the force caused by a rope,
cable, wire, string, or the like.
The Force of Tension is always in the direction
of the rope or cable, et cetera,
and the Force of Tension is always a pull,
and sometimes the symbol is just capital T.
There is also the Force Applied, F sub a,
which is just the force of one object pushing or pulling
on another object.
There is a lot we need to know about the Force of Friction,
capital F sub lower case f.
It is the force caused by the interaction
between two surfaces of two objects.
And class, what do we know about the direction
of the Force of Friction?
- The Force of Friction is always parallel to the surfaces.
- It opposes motion.
- And it is independent of the direction
of the Force Applied.
- Yes, the Force of Friction is always parallel
to the surfaces.
It always opposes motion, and what that means is
it opposes the sliding between the two surfaces.
And the Force of Friction, the direction of it
is independent of the Force Applied.
Sometimes students try to tell me
that the Force of Friction is opposite
the direction for the Force Applied,
and this is not always true.
It is true that the Force Applied
and the direction of the Force of Friction
are independent of one another.
The equation on the AP equation sheet
is the absolute value of the Force of Friction
is less than or equal to mu, the coefficient of friction,
times the absolute value of the Force Normal.
There are two types of friction.
Billy, please tell me about one of them.
- Static Friction is when the two surfaces are not sliding
relative to one another, and that equation works out
to be the Force of Static Friction is less than
or equal to the coefficient of Static Friction
times Force Normal, and therefore, the maximum Force
of Static Friction equals the coefficient of Static Friction
times Force Normal.
- Yes, the Force of Static Friction varies
in an attempt to prevent the two surfaces from sliding
relative to one another.
Bo, the other type of friction, please.
- There is also Kinetic Friction where the two surfaces
do slide relative to one another,
and then the equation is just the Force of Kinetic Friction
equals mu Kinetic times Force Normal.
- Bobby, please tell me more
about the Coefficient of Friction.
- The symbol for the Coefficient of Friction is mu,
it is determined through experiment,
it has no units.
Its value depends upon the materials
of the two surfaces which are touching one another.
The lowest value it could have is zero,
if there is no friction.
And usually the maximum is about two,
however, there could be circumstances
like drag racing tires where a mu could get up to four,
but really zero to two is a normal range
for the Coefficient of Friction.
And the Coefficient of Static Friction
is greater than the Coefficient of Kinetic Friction
for any two interacting surfaces.
That is why it is harder to get something moving
than it is to keep something moving.
- Now let's talk about Free Body Diagrams or Force Diagrams.
Free Body Diagrams or Force Diagrams
are diagrams of all the forces acting on objects.
Again, only forces appear in Free Body Diagrams.
I have five steps to help you solve
any Free Body Diagram problem.
Class, step one is
- [All] Draw the Free Body Diagram.
- Step two.
- [All] Break Forces into Components.
- Step three.
- [All] Re-draw the Free Body Diagram.
- Step four.
- [All] Sum the Forces.
- And step five.
- [All] Sum the Forces
- Again.
- One, draw the Free Body Diagram.
Do not break any forces into components
in your initial Free Body Diagram.
These instructions come directly
from the AP College Board, so I will repeat,
when you draw that first Free Body Diagram,
do not break any forces into components.
Step two, break forces into components.
Step three, redraw the Free Body Diagram.
Now, I know many of you are going to feel compelled
to skip step number three.
Please do not.
I have graded copious numbers of problems
from students where they skipped step three,
where they did not take the extra 20 seconds
to redraw the Free Body Diagram,
and they made simple mistakes.
So, please, redraw the Free Body Diagram.
Steps four and five appear to be the same.
But they are not.
You are summing the forces in two directions
which are perpendicular to one another.
Billy, what are some things you must identify
when you sum the forces?
- Every time you sum the forces,
you have to identify positive directions.
- I thought up was positive and down was negative.
- And right was positive and left was negative.
- Yeah, that is true, I guess if the direction is not clear,
you need to identify it.
Like, if there's a pulley, for example.
- Makes sense.
- Okay, okay.
- You also need to identify which object or objects
you are summing the forces on,
and which direction you are summing the forces in.
- The only time you do not have to identify
the direction you are summing the forces in,
is when you are summing the forces
in all directions simultaneously using unit vectors.
Realize the only time you can sum the forces
on multiple objects at the same time
is if all those objects have the same acceleration.
For example, if they are attached,
if they are connected via a string,
or if one object rests on top of another object.
If an object is on an incline, we will often,
though not always, break the force of gravity
into its components in the parallel
and perpendicular directions.
And instead of summing the forces in the x and y directions,
we will tip the x and y directions
so that we sum the forces
in the parallel and perpendicular directions.
And just so you know, theta in these equations
is the incline angle.
Next, let's talk about Translational Equilibrium.
Translation Motion is just when an object moves
from one location to another.
Bobby, what is the condition, what is the equation
for Translational Equilibrium?
- An object is in Translational Equilibrium
if the net force acting on the object equals zero.
- That means the object is not moving.
- Actually that's not necessarily true.
That means the object is not accelerating.
- Right, because net force equals mass times acceleration,
so if the net force equals zero,
that means the object has an acceleration of zero.
- Which means the object is either moving
at a constant velocity or is not moving at all.
- But it could be not moving.
- True, but it could be moving at a constant velocity.
- Another force we need to talk about is the Drag Force
or the Force of Resistance.
The symbol for the resistive force is F sub R or capital R,
or F sub D.
It is the force of drag caused by the interaction
between the object and the fluid
through which the object is moving.
The direction of the Drag Force is opposite
the direction of motion of the object,
and when the object is moving through the air,
this is often called air resistance.
For small objects moving at slow speeds,
the force of drag is equal to the negative
of the Proportionality Constant
times the velocity of the object.
Now, what are slow speeds and what's a small object?
Really, the only way to know
is to determine it experimentally.
So for purposes of the AP test,
they would either have to tell you it's true,
or give you information
and ask you to prove that it is true.
Bo, please give me the equation that we use most often
for the Force of Drag.
- Usually the Force of Drag equals 1/2 times capital D,
the drag coefficient of the object,
which has no dimensions, is experimentally determined,
and depends on the shape and surface texture of the object,
times rho, the density of the medium
through which the object is moving,
times capital A, the cross sectional area of the object,
normal to the direction the object is moving,
times v, the velocity of the object squared.
- A common mistake here is to use the density of the object.
Remember, rho is the density of the medium
through which the object is traveling.
Our last subject is Terminal Velocity.
Billy, what is Terminal Velocity?
Terminal Velocity is when an object moving through a fluid
has reached translational equilibrium.
May I derive the equation
for the Terminal Velocity of a object
which is falling downward in the atmosphere?
- Sure, Billy, go ahead.
- Okay, the Free Body Diagram of the object
has the force of gravity straight down,
and the resistive force straight up.
Summing the forces on the object in the y direction
equals the resistive force minus the force of gravity,
and that all equals mass times acceleration
in the y direction.
Substituting in the equations gives us
1/2 times the drag coefficient of the object
times the density of the air times
a cross sectional area of the object
times the velocity of the object squared
minus the mass of the object times
the acceleration due to gravity,
which all equals the mass of the object
times the acceleration of the object in the y direction.
We can divide by mass to solve
for the acceleration of the object.
And you can see that in the absence of air resistance,
the acceleration of the object would be equal
to the negative of the acceleration due to gravity,
as it should, because it would be in free fall.
Okay, but terminal velocity,
the terminal velocity means the acceleration of the object
is equal to zero,
so we can solve the equation for terminal velocity,
which equals the square root of two times
mass times acceleration due to gravity
divided by the quantity drag coefficient
times density times cross sectional area.
There.
We derived the equation for the terminal velocity
of an object which is falling downward through a fluid.
- Yes, however, please realize this is not the only equation
for terminal velocity.
This is the equation for terminal velocity
in this specific case.
A rocket accelerating upward, for example,
would have a different terminal velocity equation.
This brings us to the end of my review of dynamics.
Next you could enjoy my review of work, energy, and power,
or you could visit my AP Physics C Review webpage.
Thank you very much for learning with me today,
I enjoyed learning with you.