- Good morning.
Let's compare the impulse and the impact force
during three different collisions.
♫ Flipping Physics ♫
- But first, it's prom dress day.
Prom Dress Day!
- Bobby, you look very nice.
- Thank you Billy.
You do too.
- Thank you.
- Whatever.
- [mr.p] Let's start by looking
at the three demonstrations.
And now, Bo, please read the problem
and Billy, please translate.
- A racquetball is dropped on to three different substances
from the same height above each:
water, soil, and wood.
- Please stop.
Okay, a racquetball collides with water, soil, and wood
and the height initial is the same each time,
that's it so far.
- Bo, please continue.
- Rank the "blank" during the collision with each substance
in order from least to most.
Part a, impulse.
Part b, Average Force of Impact.
- Pause.
From least to most, rank impulse and average
force of impact during each collision.
- And Bo, what is that parenthetical statement?
- Assume the racquetball stops during the collision
with the water and soil.
- A velocity final for wood and soil is zero.
- Now, I know the racquetball doesn't quite stop
during it's collisions with the water and the soil.
However, the final velocity of the ball is very close
to zero and in a typical multiple choice question
you might see, the ball would be considered to stop.
So, that is what we are going to assume in this problem.
Bo, before we do anything else,
what is the equation which relates impulse to impact force?
- Impulse equals change in momentum, which equals
average force times change in time
and impulse, momentum and force are all vectors.
- Very good.
Bobby, what should we do now?
- Let's look at the different parts of the demonstrations.
There is the Free Fall portion of each demonstration,
which is from the moment you let go of the ball
to right before it strikes each substance.
Let's call that part one, so part one is Free Fall.
- For part one, each time the ball is dropped,
it starts from the same height,
so the final velocity for part one in each demonstration
is the same.
- Right after part one, the ball collides with
each substance, so we can call the collision
part two.
- And the initial velocity for part two is the same
as the final velocity for part one.
Therefore, the initial velocity for part two
for every substance is the same.
- Bo, please talk more about part two of the collisions.
- Okay, we know the ball stops at the end of part two
for both the water and the soil.
- So, the final velocity I gave before,
which equals zero is the final velocity for part two.
- Right, however, after colliding with the wood,
the ball rebounds to roughly two thirds it's initial height,
so the final velocity for part two
or the final velocity as the ball leaves the surface
of the wood must be positive.
- The racquetball is the same racquetball
for each demonstration, so, it always has the same mass.
- Thank you everybody.
It seemed logical to organize this all in a data table,
so there you go.
Let's take a look at part A, the impulse
during the collisions.
We know the impulse for part two equals the change
in momentum for part two and "change in"
means final minus initial and momentum is
mass times velocity.
So, the change in momentum for part two is mass
times velocity final for part two,
minus mass times velocity initial for part two.
Billy, what can you do with that?
- Well, we know the final velocity for part two
for both the water and the soil is zero.
Therefore, both water and soil have an impulse
of negative mass times velocity for part two initial,
so the impulse for the water and soil during the collision
is the same!
- And--
- [Bo] Mr. P?
- Yes Bo?
- Is the impulse really negative?
That would mean the impulse given to the racquetball
during the collisions is down
and that does not make any sense.
- [Mr. P] Bo, that is a good question.
Does anybody have any thoughts on that?
- The final velocity during free fall or part one
is down and therefore negative, so the impulse
ends up being positive or up.
- Right, a negative times a negative is a positive.
Thanks.
- Good and Bobby, what about the impulse for wood?
How does that compare?
- Well, the final velocity for part two for the wood
is positive, therefore, the impulse for the wood
must be greater than the impulse for the water
or the soil.
- Right because adding the positive value of
mass times velocity two final makes the impulse larger.
Yeah, that makes sense.
- So the complete answer for part A
is that the impulse during the collision with the water
is equal to the impulse during the collision with the soil,
which are both less than the impulse during the collision
with the wood.
Part B asks us to rank the force of impact
during these three collisions in order from
least to most.
Bo, please give it a try.
- Well, let's start with water and soil
because the impulse is the same
for both of those collisions.
We know impulse also equals the average force of impact
times the change in time during a collision,
so we need to compare the changes in time
during the collisions.
From the video, it looks like the change in time
during the collision with the water is much larger
than the change in time during the collision with the soil.
Therefore, because the impulse during each of those
two collisions is the same, the average force of impact
during the collision with the water
must be less than the average force of impact
during the collision with the soil.
Yeah, that makes sense.
Same impulse with a larger change in time
for the water means a smaller average force
of impact with the water than with the soil.
- Very nice Bo.
Billy, what about the average force of impact
with the wood?
- Well, we know the impulse during the collision
with the wood is greater.
So, can we just say the average impact force
must be greater as well?
- [Mr. P] I'm sorry, no.
We can't just say that.
- I think we need to compare the changes in time
during the collisions just like we did with the water
and the soil.
- Okay, let's take a look at the collisions
with the soil and the wood.
I can't tell, Mr. P.
Do you know how long each of those collisions last for?
- [Mr. Pete] Actually, honestly,
it's quite difficult to tell.
My best estimate is that both collisions last for
approximately one frame, which means
the changes in time for both the soil and the wood
are the same and it is typical of multiple choice questions
you might see to assume that these two changes in time
during these two collisions are the same.
So, that is what we are going to assume.
- Well then, because the impulse for the soil
is less than the impulse for the wood
and the two changes in time are the same,
then the force of impact for the soil must be less
than the force of impact for the wood.
- That makes sense.
There's a smaller impulse with the soil
and the same change in time for both collisions.
That makes the force of impact for the soil
less than the force of impact for the wood.
- Thank you very much for learning with me today.
I enjoyed learning with you.
A big thank you to Jan Wery and Judi Lintott
of The Ann Arbor Prom Dress Project
for lending me these awesome prom dresses.
They sell gently used prom dresses at very reasonable prices
because they feel every young lady should be able
to afford a prom dress.
You can find more information about
The Ann Arbor Prom Dress Project
in the description of this video, thanks.