- Good morning.
The symbol for gravitational potential energy is
- ♫ Flipping Physics ♫
capital PE with a subscript of g.
Sometimes you will see it as a
capital U with a subscript of g.
However, I prefer PE for potential enery
with a subscript of g for gravitational.
Gravitational potential energy,
the energy stored in an object
due to that objects elevation.
In other words, if I lift this book upward,
it gains gravitational potential energy,
which is the potential to become other types of energy.
For example, when I drop the book,
it becomes kinetic energy as the book falls.
Gravitational potential energy equals
m times g times h
where m is the mass of the object,
g is the acceleration due to gravity,
which, Bobby, on planet Earth is
- 9.81 meters per second squared.
- [Mr. P] Positive or negative?
- Positive.
- [Mr. P] Are you positive?
- Absolutely.
- The acceleration due to gravity here
on planet Earth is positive 9.81 meters per second squared.
- And h is the vertical height
above the horizontal zero line.
And the horizontal zero line is
a zero reference line that you,
the person solving the problem,
get to decide the location of.
- Oh good!
We get to decide where the horizontal zero line is.
Yay!
- [Mr. P] Now we need to discuss
the horizontal zero line specifically.
In order to do so, let's pretend
that I'm very small and standing on this dictionary.
Now, we can set the horizontal
zero line wherever we want to,
and we have to identify the location
of the horizontal zero line every time we solve a problem
which includes gravitational potential energy.
- Why did he change his shirt?
- It's green.
- Oh...
- ♫ ha ha ha ha ♫
(laughs)
Yeah, I kind of disappear don't I?
Let's start by setting the horizontal
zero line as low as we can on the screen.
Now considering we are talking about
my gravitational potential energy,
which we calculate using my vertical
height about the horizontal zero line,
which is the vertical displacement
from the horizontal zero line to my center of mass,
is my vertical height above the zero line, class,
positive, negative, or zero?
- Positive.
- Then with the horizontal zero line
near the bottom of the screen,
because my vertical height above
the horizontal zero line is postive,
I currently have positive gravitational potential energy.
If we move that horizontal zero line
up toward the top of the screen, class,
now is my vertical height above the zero line
positive, negative, or zero?
- Negative.
- Therefore, with the horizontal zero
line near the top of the screen,
because my vertical height above
the horizontal zero line is negative,
I currently have negative gravitational potential energy.
So, notice, gravitational potential
energy can be negative if the object
is located below the horizontal zero line,
and, therefore, has negative vertical height
above the horizontal zero line.
Okay, now, what if we move the
horizontal zero line to my center of mass?
Class, is my vertical height above
the horizontal zero line positive, negative, or zero?
- Zero.
- Therefore, if the object is located
at the horizontal zero line,
because the vertical height above
the horizontal zero line equals zero,
the gravitational potential energy
associated with that object is, then, zero.
So, notice how the gravitational
potential energy of an object is very
much dependent on the location
of the horizontal zero line.
And who, class, decides where the
horizontal zero line is for a problem?
- We do.
- Therefore, you need to identify
the location of the horizontal zero line
when you are working with gravitational
potential energy every time.
- Every time.
- Every time?
- Every time.
- Every time?
- [Mr. P] Every time.
Yes, every time you work with gravitational
potential energy you have to identify
the location of your horizontal zero line.
- Yep.
- Yep, I got it.
- Every time.
- Okay, let's pretend I'm back to my normal size.
[buzzing]
And standing on the floor.
Please realize we rarely move the
horizontal zero line in the middle of a problem.
We moved it around today to help
you understand the concept of the
horizontal zero line, but again,
please don't move it around during a problem.
And, typically, we place the horizontal
zero line either at the ground
or the lowest location an object will be.
Typically, but not always, of course.
Gravitational potential energy is a scalar.
Bo, could you please determine its units?
- Mass is in kilograms,
acceleration is in meters per second squared,
and height is in meters.
So, kilograms times meters per second squared
is Newtons, so Newtons times meters, which is joules.
Gravitational potential energy is in joules.
- Great!
Thank you very much for learning with me today.
I enjoyed learning with you.
- Two dollars.