mr.p: Think you are wearing your helmet?
Think again.
Bo: Hey guys. Billy: Hey Bo.
Bobby: Hi Bo.
♫ Flipping Physics ♫
mr.p: I often see people pretending to wear helmets.
So I want to talk about how and why to wear one.
Let's start with the basics.
It's pretty clear that the guy on your left
is wearing a helmet and the guy on your right
is not wearing a helmet.
But how about now?
Bo, is the guy on your right wearing a helmet?
Bo: Pfff duh, it's on his head, so he's wearing a helmet.
Bobby: Actually if you look closely you can see
that the helmet is actually not strapped to his head.
[Billy] Yeah, so without the helmet strapped to his head,
he's not really wearing it.
[Bo] Really? The helmet is on his head,
so what difference does it make?
mr.p: Bo, I'm guessing that you are not alone in your assumption
that it doesn't really matter whether you buckle the strap
or not on your helmet.
So I decided to illustrate what happens if you do not
buckle the strap on your helmet.
Everybody ready?
I decided to ride my bike off a dock, into a lake.
Here we go!
First with the helmet buckled,
and then with the helmet not buckled,
to illustrate the difference.
Now please, enjoy.
Pay careful attention to what happens to the helmet,
and please do not try this at home.
(upbeat music)
Billy: Yeah, it was really neat.
Bo: Nice form.
Bobby: That was really good, Mr. P.
mr.p: Thank you, but the important thing is to notice
what happens to the helmet when the strap isn't buckled.
The helmet doesn't stay on your head.
But, what does it matter,
I mean I just landed in the lake, right?
So, let's talk about what would be different
if I instead did this on concrete.
Billy: I think that would hurt.
Even if you were wearing a helmet.
mr.p: But if you're not wearing your helmet,
it can actually be deadly.
To understand why, let's start with Newton's Second Law.
Bo, could you please tell me what is Newton's Second Law?
Bo: F equals ma.
Bobby: Really Bo, we use words in this class, not letters.
You know that.
Bo: Force equals mass times acceleration.
Billy: And don't forget, force and acceleration are both vectors.
Bobby: And it's the net force, not just force.
Bo: Okay, net force equals mass times acceleration,
where both force and acceleration are vectors.
mr.p: That is correct, however,
I actually need Newton's Second Law in terms of momentum.
Which is the net force equals
the change in momentum over change in time,
where both force and momentum are vectors.
Delta, or change in, always means final minus initial.
So the change in momentum is equal to
the final momentum minus the initial momentum.
And momentum equals mass times velocity,
therefore we end up with the net force
is equal to mass times velocity,
final minus mass times velocity initial,
that whole quantity divided by the change in time.
Yes, Bobby?
Bobby: Couldn't we also have gotten to that equation
using mass times acceleration?
Because acceleration equals
the change in velocity over the change in time.
And change in velocity
is the final velocity minus the initial velocity,
and then multiplying through by mass
gives us the same equation.
Net force equals mass times velocity final
minus mass times velocity initial,
all divided by the change in time.
[Mr. P.] Very nice, Bobby.
Before we start analyzing the equation,
I want to point out that we're going to use
the impulse approximation for the net force.
The impulse approximation is the basic idea
that during the short time interval of the collision,
the force of impact is much larger
than all of the other forces.
Therefore, we can consider the other forces
to be negligible when compared to the impact force.
And the net force is approximately equal
to the force of impact.
Lastly, let's multiply both sides by the change in time.
We end up with the force of impact times the change in time
is equal to the mass times velocity final
minus mass times velocity initial.
Now, I want to start
with just the right hand side of the equation.
And let's discuss how these variables change depending on
whether I'm wearing my helmet or not wearing my helmet.
So again, we're gonna look at this right hand side,
and see how these variables change,
depending on whether I buckled the helmet strap
or did not buckle the helmet strap.
Let's start with the mass.
Bo, what is the mass and does it depend
on whether the helmet is on my head or not?
Bo: This is the impact force of your head,
so I guess that would be the mass of your head.
No, adding a helmet to your head
doesn't really change the mass of your head very much.
mr.p: Correct.
The mass will remain the same,
regardless of whether I'm wearing my helmet or not.
Bobby, let's talk about the velocity final after the impact.
What is it and how does it change
depending on helmet status?
Bobby: Your head should pretty much stop after the collision,
regardless of whether the helmet is on your head or not.
So the velocity final is zero
and does not depend on if the helmet is on your head.
mr.p: Lastly, what about the velocity initial,
right before the collision.
Billy?
Billy: Well, how fast you're going before the collision
should be the same,
regardless of whether you are wearing a helmet or not.
mr.p: So notice that the entire right hand side of the equation
does not change
depending on whether I'm wearing my helmet or not.
This is actually the concept of impulse.
Impulse is equal to the change in momentum.
Remember mass times velocity final
minus mass times velocity initial
was equal to the change in momentum.
And that is also equal to the force of impact
times the change in time.
And remember, none of these variables
depend on whether I'm wearing my helmet or not.
Which means the impulse also does not depend
on whether I'm wearing my helmet or not.
Which means that the product
of the force of impact and the change in time
will not change depending on
whether I'm wearing my helmet or not.
So, what does wearing a helmet
do to the change in time during a collision.
Bo: Oh, the helmet increases the distance
over which your head stops, and therefore
increases the time necessary to stop your head.
Bobby: Yeah, right.
So if the change in time is increased,
the impact force is decreased.
Billy: Because the product
of the change in time and the impact force remains constant.
[Mr. P] Correct.
If I do not wear a helmet, the change in time is very small,
which makes the force of impact very large.
That means when I do wear a helmet,
the change in time is larger,
which decreases the force of impact.
This is actually the same way that airbags,
seatbelts, bubble wrap and crumple zones work.
They all increase the time during the collision,
to decrease the force of impact.
And, so you know, this isn't all just theoretical.
When I was 15 years old,
I was riding my bike down a hill very quickly.
I accidentally got the whole bike on the gravel shoulder.
I tried to get the whole bike back onto the road,
but I didn't do it,
I only got the front tire back onto the road.
The back tire was stuck in the gravel.
And this actually caused the whole bike to flip,
and threw me onto the road.
This is one of those memories that you have
that's like permanently stuck in your brain.
I can actually still see the bike
as it went over the top of me.
And I can remember grabbing the bike
and dragging it off of the road.
And I remember pulling off the helmet,
and looking at the helmet
and seeing a huge chunk taken out of the helmet.
Which was amazing, because the helmet had done
exactly what it needed to do.
It had increased the time during the collision
and therefore decreased the force of impact
between my head and the road.
And I was fine.
Bo: I bet you were glad that helmet was strapped to your head.
[Mr. P.] Absolutely, but let's take a moment
to contrast my story with the story
of a high school friend of mine,
who was an experienced BMX biker and was riding his bike
down a hill in the evening, again moving very quickly.
And a raccoon darted out in front of him,
and his front tire ran into that raccoon.
He ended up being launched from the bike,
landed on the concrete, fractured his skull,
and he spent a long time in the hospital.
Three days of which he was in an induced coma
because they were concerned about his brain swelling.
He did eventually fully recover,
however he does have a lump on his skull
to remind him that wearing a helmet is a very good idea.
So, please buckle your helmet.
The last thing you want to happen
is for your helmet to come off just the moment you need it.
Please wear and buckle your helmet.
Thank you very much for learning with me today,
I enjoyed learning with you.