Bo: Hey guys.
Billy: Hey, Bo.
Bobby: Hi, Bo.
♫ (lyrics) Flipping Physics ♫
Mr. P: Ladies and gentlepeople,
the bell has rung, therefore class has begun,
therefore you should be seated in your seat
ready and excited to analyze a video taken on the moon.
Billy: Cool.
Bobby: Which moon?
Our moon?
Bo: Yeah, our moon.
Mr. P: Yep.
In order to show that the acceleration due to gravity
is independent of mass, in 1971 NASA filmed
astronaut David Scott holding a feather
and a hammer at the same height
and dropping them at the same time.
Let's enjoy the video.
David: I wanna watch this.
A good picture there. I've got ...
Operations: Beautiful picture, Dave.
David: In my left hand I have a feather.
In my right hand a hammer.
I guess one of the reasons we got here today
was because of a gentlemen named Galileo
a long time ago who made a rather significant
discovery about falling objects and gravity fields.
And we thought that, where would be a better place
to confirm his findings than on the moon?
And so we thought we'd try it here for you.
The feather happens to be, appropriately,
a falcon feather for our Falcon,
and I'll drop the two of them here and hopefully
they'll hit the ground at the same time.
How about that?
Operations: How about that?
David: I think that proves that Mr. Galileo
was correct in his findings.
Mr. P: So now what we're gonna do,
is we're gonna take a look at the video
and figure out variables that we know
and see what we can calculate from there.
So, Bobby, taking a look at the video,
which I have now looped to just show
the dropping of the objects, tell me
a variable that we know.
Bobby: It looks like ...
Is their initial velocity zero?
Mr. P: Yes, the initial velocity in the Y direction
is equal to zero because he drops the hammer
and the feather.
Bo, what else?
Bo: We know from the last lecture
that the acceleration due to gravity on the moon
is about 1/6th of what it is here on earth, right?
Mr. P: Correct, however more specifically
it's the acceleration due to gravity on the moon
that is 1.62 meters per second, squared.
And, therefore, the acceleration in the Y direction,
which is equal to -g, is equal to -1.62
meters per seconds, squared.
Uh, Billy, what else do you see?
Billy: Isn't the frame rate of standard
definition video 29.97 frames per second?
So, can't we just figure out the number of frames
to determine how long it fell for?
Mr. P: Absolutely right.
Very nice, Billy.
The National Television System Committee,
or NTSC, standardized the color television
broadcast signal in the United States in the 1950's
to have a frame rate of 29.97 frames per second.
And this is clearly after the 1950's
and is before high definition video.
I wasn't even born in 1971.
So let's go through and count the frames.
David: Well, in my left hand I have a feather.
In mt right hand, a hammer.
And I guess one of the reasons we got here today
was because of a gentleman named Galileo
a long time ago, who made
a rather significant discovery. Operations: Superb!
Mr. P.: So there you go, 36 frames.
We need to convert the change in time
from frames into seconds.
Billy pointed out that there are
29.97 frames per second in this video,
therefore we're gonna multiply our change in time
by the reciprocal of the frame rate.
And what do we get for our change in time?
Bobby: It's 1.201201 seconds.
Mr. P: And given that information
we can figure out the initial height above the ground
from which Mr. Scott droped the hammer and feather.
Bo, how can we figure out the height initial?
Bo: Well, the acceleration is constant,
so we can use our uniformly accelerated
motion equations, we just need to pick the right one.
Let's use the displacement equals the velocity
initial, times the change in time, plus one half,
times the acceleration, times the change in time, squared.
We have all the numbers and the initial velocity
is zero and anything times zero is just zero,
so the displacement equals 1/2, times -1.62,
times 1.201201 squared, which gives us ...
-1.16874 and using two sig figs
because our frame rate only had two sig figs,
so that rounds to -1.2 meters.
Mr. P: Very nice, Bo.
One thing to notice that I did, is I added Y's to make sure
that we identify that this is all in the Y direction.
Oh, for those of you who are still using English units,
because there are 3.281 feet per meter,
we can do this.
Which means that Mr. Scott dropped the hammer
and the feather from an initial height
above the ground of approximately 1.2 meters
or 3.8 feet, which is approximately this high,
which looks pretty close to me.
Yes, Bobby, you have a question?
Bobby: Mr. P, where did the negative go?
Mr. P: Oh, right, okay, so the delta Y,
or displacement, has both magnitude and direction
and because the hammer and feather
were going down this means that the
displacements were negative.
However, I asked for the heights initial
above the ground, which is a positive number.
Any other questions?
Billy: No.
Bobby: Cool video.
Mr. P: In that case, realize that we just took
a video that was filmed in 1971 on the moon,
which has almost no atmosphere and therefore
the hammer and the feather were truly in free-fall.
We counted the frames to figure out how long
they were in free-fall and used a UAM equation
to figure out the height initial
for the hammer and feather above the ground.
I think that's pretty cool.
Thank you very much for learning with me today.
I enjoyed learning with you.