- Good morning.
The symbol for elastic potential energy is...
♫Flipping Physics♫
Capital PE with a subscript of e.
Sometimes you will see it, instead, as a capital U
with a subscript of e.
However, I prefer PE for potential energy
with a subscript of e for elastic.
Elastic potential energy is the energy stored
in an object due to the temporary deformation
of that object.
There are all sorts of examples of elastic potential energy
where we store energy in that object
due to the temporary deformation of that object
and the most common example is a spring.
If we compress the spring, if we make it smaller,
elastic potential energy is stored in the spring
and can be converted to kinetic
and gravitational potential energy.
We can also elongate the spring.
We can make it longer.
Again, elastic potential energy is stored in the spring
and can be converted to kinetic
and gravitational potential energy.
Elastic potential energy isn't only stored in springs.
This toy, for example, stores elastic potential energy
in this rubber band.
And this rubber ball stores elastic potential energy
when it strikes the ground.
As the ball is compressed, it stores elastic
potential energy.
That elastic potential energy is then converted
to kinetic energy and gravitational potential energy
as the ball regains its spherical shape and moves upward.
Billy, the equation for elastic potential energy, please.
- Elastic potential energy equals one half k x-squared
where k is the spring constant of the spring
and usually has dimensions of Newtons per meter
and x is the displacement from equilibrium position.
- Sometimes the equilibrium position is called
the rest position.
- How do you guys know all this stuff?
- We did our homework.
- Yeah, it helps.
- Oh!
- The spring constant is a measurement
of how much a spring resists displacement.
More specifically, the spring constant is how much force
it takes to compress, or expand to the spring per meter.
For example, this weak spring has a small spring constant
of about 65 Newtons per meter
because it takes very little force to compress it.
And this strong spring requires a lot more force
to compress it because it has a large spring constant
of about 3,300 Newtons per meter.
Now, what do you think about the spring constant
of this Slinky?
Bo, is this a large or a small spring constant?
- Well, it looks like it's pretty easy to deform the Slinky
so it must have a small spring constant.
- That is correct Bo.
And what about this Pogo stick, Billy?
Do you think this spring inside this Pogo stick
has a large or a small spring constant?
- Well, when you bounce on the Pogo stick,
it looks like it probably applies a pretty large force
to the spring, so that spring must have
a large spring constant.
- That is correct, Billy.
Now let's go through an example where we analyze
the elastic potential energy stored in this rubber band.
Okay, you can see I have the rubber band attached
to the force sensor and if I...
- Do you mind if I help?
- Hey there Mr. Fullerton.
Actually, that would be great!
Go ahead.
- Thanks.
Let's start with the rubber band at equilibrium,
or rest position.
This is where the force of the spring,
or, in this case, the rubber band is zero.
You can see that is where the right end
of the rubber band is currently.
- Who is that?
- That is Mr. Fullerton of APlusPhysics.com.
- You were in one of his videos.
- As Mr. P pulls the rubber band to the right
the displacement from equilibrium position, or x, increases
and the force caused by the spring increases linearly
which you can see in the graph.
The slope of the line which describes this data
is the spring constant of the rubber band.
For this rubber band, the slope of the line,
and, therefore, the spring constant is 241
Newtons per meter.
Wait. Have you discussed Hooke's Law yet?
Can I even say all that?
- No, actually we haven't yet defined the force of a spring
or Hooke's Law.
So let's not do that.
Why don't you just give us the spring constant, please?
- Okay. Never mind about the graph.
Let's just say I took measurements
to get the spring constant of the rubber band
which is 241 Newtons per meter.
- I feel like I just learned something
I wasn't supposed to yet.
- Yeah.
- Let's determine the elastic potential energy stored
in the rubber band when it is elongated
by 12 centimeters, or 0.12 meters.
Actually, Bobby, would you mind doing that for us?
- [Bobby] Sure!
- Thanks.
- Well, elastic potential energy is
one-half the spring constant times the displacement
from equilibrium position squared.
So it equals one-half
times 241
times 0.12 squared
which is 1.7352 or 1.7
with two significant digits.
But what are the units?
- Joules.
- I bet we actually have to determine the units.
- [Mr. P] Yes, absolutely. - [Mr. F] Yes, absolutely.
- [Mr. P] Jinx. - [Mr. F] Jinx.
- [Mr. P] You owe me a soda. - [Mr. F] You owe me a soda.
- Yeah, okay.
Well, the spring constant is in Newtons per meter
which is multiplied by meters-squared.
Meters cancel out and we are left
with Newton-meters which is Joules.
So the energy stored in the spring is 1.7 Joules.
- I do need to write stuff on the board now,
so I do need to let go of the force sensor.
So, thank you very much for your help, Mr. Fullerton.
- You;re very welcome.
My pleasure. Any time.
- I want my two dollars.
(air blowing)
Wooooo!
- Goodbye everyone.
Make it a great day.
- Did anyone else find that floating head disturbing?
- No.
- Nope.
- Bo, considering the spring constant
cannot be negative, can you have negative
elastic potential energy?
- The displacement from rest position can be negative.
However, it is squared.
So, no, you cannot have negative elastic potential energy.
- Thank you Mr. Fullerton of APlusPhysics
for your help today.
And thank...
Oh hold up. I'm sorry.
I totally forgot to mention that like kinetic energy
and gravitational potential energy,
elastic potential energy is a scalar.
But now I did just mention it.
So, never mind about that apology.
Sorry. Wait. No. Bye.
You for learning with me today.
I enjoyed learning with you.