Mr. P: Good morning.
Today we are going to understand the reality
behind some common mistakes or misconceptions
students have about objects in free fall.
Here we go!
Bo: Hey guys.
Billy: Hey Bo!
Bobby: H-hi Bo.
♫ (lyrics) Flipping Physics ♫
Mr. P: Let's start with a quick review
to make sure we're all on the same page.
Bo, could you please remind me, how do we
identify an object in free fall?
Bo: An object in free fall is one that isn't touching
anything else and there can't be any air.
Mr. P: True.
I like to call it being in the vacuum that you can breathe.
And Billy, what do we know about an object
that's in free fall on Earth?
Billy: Little g, or the acceleration due to gravity
on Earth, is positive 9.81 meters per second squared.
And the acceleration in the y direction
is equal to negative g, so the acceleration is
negative 9.81 meters per second squared.
Bobby: Or 9.81 meters per second squared down.
Mr. P: Great.
And remind me, class.
Is the acceleration due to gravity,
little g, positive or negative?
All: Positive.
Mr. P: And this makes the acceleration
in the y direction for an object
in free fall positive or negative?
All: Negative.
Mr. P: Great.
The first misconception is that
if I throw this ball upward, then when it is moving upward,
because the velocity is positive the acceleration
would also be positive and therefore it would be
a positive 9.81 meters per second squared.
Bobby, please explain why this is incorrect.
Bobby: Uh, well, we know the ball will slow down
as it moves upward, therefore the direction
of the acceleration needs to be opposite
to the direction of the velocity.
Therefore, because the velocity is upward and positive,
the acceleration must be downward and negative.
Mr. P: Exactly, Bobby.
The ball slows down on the way up.
So the acceleration is opposite
to the direction of the velocity,
therefore the acceleration is down and negative.
Who can explain to me what would happen
if the acceleration were positive on the way up?
Bobby: Uh, the ball would shoot upward like a rocket.
Right?
Mr. P: Yep. (suspenseful sound effects)
If the acceleration were positive,
the ball would accelerate upward like a rocket.
Just like this.
(explosion sound effect)
(laughs)
Billy: Wow!
Bo: Woah.
Bobby: Cool.
Billy: Yeah, I don't think that's possible.
Mr. P: Next.
Sometimes students tell me that the initial velocity
for an object being thrown upward is zero.
I love this, because then I get
to show an object being thrown upward
with an initial velocity of zero.
Watch.
(anticipatory sound effects)
(Mr. P grunts in effort)
(laughs)
See, it won't go anywhere.
Bobby: Yeah, that's not going to go up very far.
Mr. P. Right.
An initial velocity of zero will not
cause an object to move upward.
In fact, the initial velocity in the y direction
must be positive in order for an object to move upward.
Another misconception is that if I drop a ball,
and if I take a ball and I throw it downward,
that the ball that I threw downward
will have an acceleration downward
that is larger than if I just drop the ball.
Billy, please help dispel this misconception.
Billy: Well, we know the dropped ball
and the ball thrown downward will both have accelerations
of negative 9.81 meters per second squared,
because they are both objects in free fall.
So I don't really see why people
would think the thrown one would accelerate more.
Bo: Uh, Billy, can I give it a try?
Billy: Sure, Bo, go ahead.
Bo: I think it's because people
often confuse velocity and acceleration.
The ball that is thrown is moving faster,
however, its velocity is not changing faster.
So it must be because people see the ball moving faster
they assume it must be accelerating more quickly.
Right, Mr. P?
Mr. P: Yes, Bo, very nice.
The thrown ball is moving faster,
therefore people think it is accelerating faster.
However, it is not.
As Billy pointed out, both objects
are objects in free fall, and therefore both
have an acceleration in the y direction
of negative 9.81 meters per second squared.
OK, remind me, Billy, what is the velocity
in the y direction for an object
in free fall at the very top of its path.
Right there.
Billy: The velocity at the top in the y direction is zero.
Mr. P: And Bobby, please explain
to me one reason we know why.
Bobby: Um, on the way up the velocity is positive,
and on the way down the velocity is negative,
so at the top the velocity must be zero.
Mr. P: Which leads us to our last misconception.
Class, what is the acceleration in the y direction
of the ball at the very top of its path?
Again, right there.
All: Uh...
Billy: Zero!
Bobby: Negative 9.81 meters per second squared.
Mr. P: Right, which is why we need to talk about this.
Class, when the ball is at the very top
of its path, is it touching anything?
All: No.
Mr. P: Is it in the vacuum that you can breathe?
All: Yes.
Mr. P: Then is it in free fall?
All: Yes.
Mr. P: Then its acceleration is...
All: Negative 9.81 meters per second squared.
Billy: But it's velocity is zero,
so its acceleration must also be zero.
Mr. P: It is very common to assume
that because the velocity at the top
of the path is equal zero, then also
the acceleration must be equal to zero.
This is not true.
To help us to understand why, let's start
with the equation definition for acceleration.
Please, Billy?
Billy: Acceleration equals change
in velocity over change in time.
Mr. P: I think it's safe to assume
that time doesn't stop, therefore the change
in time is not going to be equal to zero.
Therefore if the acceleration at the top
is equal to zero, then the change in velocity
at the top must also be equal to zero.
Therefore, the velocity would not change
at the top if the acceleration
at the top were equal to zero.
So, Billy, explain to me what would happen
if the acceleration at the top
in the y direction were equal to zero.
Billy: Oh, it would stop in mid-air, and just float!
Because if the velocity is zero at the top
and the velocity isn't changing,
then the velocity would continue
to stay zero and the ball would just float there!
(dramatic sound effect)
Mr. P: Right.
It would look like this.
(eerie sound effects)
Eh?
I know.
Bo: Awesome.
Bobby: Mr. P, that's cool.
Billy: Wait, I thought it wouldn't do that!
Mr. P: Therefore, the acceleration clearly isn't zero...
Sorry. (claps hands)
And it is an object in free fall,
therefore the acceleration in the y direction
is negative 9.81 meters per second squared.
Any questions?
Bobby: Nope, I'm good.
Bo: No, I got it.
Billy: I think I'm OK.
Mr. P: So ends our common free fall pitfalls lesson.
Let's do a quick review.
First off, for an object going up,
the acceleration is still negative.
For an object thrown upward, the initial velocity
in the y direction must be greater than zero.
For an object thrown downward,
again, it's still in free fall, so the acceleration
is negative 9.81 meters per second squared.
Yes, it's moving faster, but it's not accelerating more.
The velocity at the top in the y direction is equal to zero.
And lastly, the acceleration at the top
is still negative 9.81 meters per second squared,
because it's an object in free fall, regardless of the fact
that the velocity at the top is equal to zero.
Thank you very much for learning with me today,
I enjoyed learning with you.