mr.p: Good morning!
Today we are going to review the topics of
work, energy, power and Hooke's law,
which are covered on the AP Physics 1 exam.
Bo: Hey guys.
Billy: Hey Bo!
Bobby: Hi Bo.
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mr.p: From the equation sheet.
In terms of an object or a group of objects,
which we call the system.
The change in energy of the system equals
the work done on the system.
Which is equal to the force doing that work
times the displacement of the object times the cosine
of theta, where theta is the angle between the direction
of the force and the direction
of displacement of the object.
In other words, work causes a change in energy
of a system.
We'll talk more about that energy in just a bit.
Let's concentrate now on the work equation.
Bobby: Mr. P?
mr.p: Yes, Bobby?
Bobby: What is the force parallel times displacement?
mr.p: Oh, right.
The force parallel to the displacement equals
the force times the cosine of theta.
Remember to always identify which force you're using
in your work equation.
And it could be the net force.
In which case you could substitute in mass
times acceleration using Newton's second law.
And remember to only use the magnitude
for the force and the displacement.
It is the cosine of the angle theta,
which determines whether the work is positive or negative.
Bo, what are the dimensions for work?
Bo: Work is in joules.
mr.p: And what is a joule?
Billy: A joule is a Newton times a meter.
Bo: Yeah, a joule is a Newton meter.
mr.p: Bobby, please tell me everything you know
about one of our three types of mechanical energy.
Bobby: Kinetic energy is the energy of motion.
The equation is kinetic energy equals one-half
times the mass the object
times the velocity of the object squared.
And kinetic energy will never be negative
because mass can't be negative and the velocity is squared.
mr.p: I prefer to use KE instead of K for kinetic energy
because K can stand for the spring constant,
Boltzmann's constant, the dielectric constant,
Kelvin's or even 1,000.
So I prefer KE for kinetic energy.
Billy, could you please tell me everything you know
about another type of mechanical energy?
Billy: Elastic potential energy is the energy stored
in a spring or an elastic or stretchy material
like a rubber band.
Elastic potential energy equals one-half
times the spring constant times the displacement
from the equilibrium position or the rest position, squared.
The spring constant is a measurement of how much
force it takes to compress or expand a spring.
And the equilibrium or rest position
is where the spring will be in equilibrium
without other forces acting on it.
And just like kinetic energy, elastic potential energy
will never be negative because the spring constant
can't be negative.
And the displacement from equilibrium position is squared.
mr.p: Very nice.
Again, I prefer PE sub e for elastic potential energy.
But U sub s can work too.
Bo, the last type of mechanical energy, please.
Bo: Gravitational potential energy is the energy
associated with a gravitational field
like the one we live in. It equals the mass of the object
times the acceleration due to gravity
times the vertical height above the horizontal zero line.
You have to identify a horizontal zero line
before you begin a problem.
Gravitational potential energy can be negative
if the object is below the horizontal zero line,
which would make the vertical height
above the zero line negative.
And we should remember that work and energy are scalars.
mr.p: Right, again I prefer PE sub g
for gravitational potential energy.
And also, I usually refer to it in terms of
absolute gravitational potential energy rather than
a change in gravitational potential energy.
This equation is for the gravitational potential energy
in a constant gravitational field.
We'll get to the gravitational potential energy
in a non-constant gravitational field in just a little bit.
Bobby, what are the dimensions for energy?
Bobby: Well, we know work and energy
have the same units, so joules.
mr.p: Really, Bobby.
Can you prove that?
Please start with the equation for kinetic energy.
And prove to me that is in joules.
Bobby: Okay.
Kinetic energy equals one-half mass
times velocity squared so its dimensions
are mass in kilograms.
And velocity is in meters per second.
And velocity is squared, so its kilograms
times meters squared over seconds squared.
mr.p: And that works out to be joules?
Billy: Yes, because that equals kilograms times meters
over seconds squared times meters.
So you can substitute in Newton's for kilograms
times meters divided by seconds squared.
And you get Newtons times meters, which is joules.
mr.p: Very nice.
Conservation of mechanical energy.
The total mechanical energy initial
equals the total mechanical energy final.
Billy, when and how can we use conservation
of mechanical energy?
Billy: Mechanical energy is conserved in the absence
of non-conservative forces.
In other words, when there is no friction.
Bobby: You mean no energy converted to heat, light or sound
via the sliding friction between two surfaces, right?
Billy: Right and before we use the conservation
of mechanical energy equation, we need to
specifically identify the initial and final points.
We also need to identify the horizontal zero line.
Then we identify which types of mechanical energy
are present at the initial and final points.
Substitute in those equations and solve the problem.
mr.p: Remember as well that you can't have energy
added to the system via a force applied and still use
conservation of mechanical energy.
Now, what if you need to use energy.
However, energy is being converted
to heat, light or sound via friction?
What do you do then?
Bo: Then we go back to the work equation.
The work due to friction equals the change
in mechanical energy of the system.
For the work due to friction, substitute in the force
of friction times the displacement
times the cosine of the angle
between the force of friction and the displacement.
Which should be 180 degrees.
Because the force of friction opposes motion.
And that equals the mechanical energy final
minus the mechanical energy initial.
We need to identify the initial and final points.
And the horizontal zero line.
That assumes that there is no energy
added or removed from the system via force applied.
If there is, then we also need to include the work done
by the force applied with the work done
by the force of friction.
mr.p: Very nice.
Now let's talk about the rate at which work is done.
Which is called power.
Power is simply how long it takes to change
the energy of the system or how long it takes to do work
on the system.
And we can also substitute in the equation for work.
And because d over delta t or the displacement
over change in time is velocity, we now have
an equation for power in terms of velocity.
And remember, just like the work equation,
you need to identify which force is doing the work.
And theta is the angle
between the direction of the force and the direction
of the velocity of the object.
Bobby, what are the dimensions for power?
Bobby: Power is in joules per second, which are called watts.
mr.p: Also 746 watts is equivalent to one horsepower.
You certainly don't need to memorize that.
However, it's good to be familiar with the term.
Now, let's talk about Hooke's law.
Hooke's Law, the force of a spring is linearly proportional
to the displacement from equilibrium position.
In other words, the force of the spring is equal
to the spring constant multiplied by that displacement
from equilibrium or what is also called rest position.
And if you make a graph of the force of a spring
versus the displacement from equilibrium position,
the slope of the best fit line will be the spring constant
of the spring.
Which brings us to typical dimensions
for the spring constant.
The spring constant is in force per unit length.
Therefore, Newtons per meter.
This brings us to the end of my review lesson
on work, energy and power for AP Physics 1.
My next review lesson is
about linear momentum and impulse.
You are welcome to enjoy that video.
You can also go to my Website flippingphysics.com,
where you can find all of my AP Physics 1 review
videos organized with lecture notes.
Thank you very much for learning with me today.
I enjoyed learning with you.