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Physics: Impulse and Newton's Second Law 12 Views
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Description:
What is Newton's Second Law, and how long do you go to prison if you break it? Long enough to study friction, buoyancy, closed systems, and more.
Transcript
- 00:00
All right impulse and newton's second law the best pairing
- 00:04
since pb met jay did you fire him over when
- 00:10
and where A sound for buoyancy girl and seeing their
- 00:15
kids all right you're in second launching for men and
- 00:19
a funny thing emoji rico's graphic impulsive way her pg
Full Transcript
- 00:27
thirteen site way legal we do ok moving on every
- 00:33
sport involves physics just think of the parappa ulla of
- 00:36
a basketball when steph curry shoots a halfcourt buzzer beater
- 00:41
for how when ah hockey player is checked into the
- 00:44
boards the boards push back on the player just as
- 00:47
hard as he slams into them or how the acceleration
- 00:51
of gravity can really ruin a gymnast day in their
- 00:55
most sports fans don't think about any of that stuff
- 00:57
when they're watching the game but if you're a physicist
- 01:00
while sometimes it feels like all you can see is
- 01:03
physics not ghosts but when you're actually playing a sport
- 01:06
you're going to be in big trouble if you've got
- 01:08
physics on your brain like when you're standing in the
- 01:11
batter's box looking to hit a walk off home run
- 01:14
well if you're thinking about how your bat's going to
- 01:16
change the balls Momentum Chances are pretty good that the
- 01:18
only thing you'll be hitting our some molecules in the
- 01:21
air But once you start thinking about this stuff well
- 01:24
it's hard to stop After all the system between the
- 01:26
batter the baseball bat and the ball itself is about
- 01:30
as close is will come to having a closed system
- 01:33
here on earth In physics terms a closed system is
- 01:37
where no matter enters or leaves the system and there
- 01:41
are no effects from forces outside of the system Got
- 01:45
that All right Well if i'm trying to catch a
- 01:47
foul ball and some jerk in the stands feels a
- 01:50
soda on me He's just introduced some matter into the
- 01:53
system made up of me and the ball Some very
- 01:57
cold sticky matter And i'm not happy about it All
- 02:00
right Well even in the system when i'm up to
- 02:02
bat there is still the force of gravity that's pulling
- 02:05
on everything And everyone on the ball also has to
- 02:09
deal with drag In fact it's pretty much impossible to
- 02:12
find a true closed system Of course if you could
- 02:15
consider the whole universe to be one big fat close
- 02:18
System Well that'd be a different thing but you hate
- 02:21
to see the equation for conservation of momentum in that
- 02:24
system Pretty big Well here on planet earth many things
- 02:27
can enter into a closed system Like the force of
- 02:31
friction We can all use sorts of goop to reduce
- 02:34
friction Yeah but we could never make it go away
- 02:37
completely And if you go bowling underwater while you're gonna
- 02:41
be dealing with drag and buoyancy so if you're hoping
- 02:44
to get a strike in the bikini bottom bowling alley
- 02:47
when well it'll take a lot more room than on
- 02:48
dry land So how do we figure out mo mentum
- 02:51
when there's an outside force messing with it Well luckily
- 02:54
for us some guy named isaac newton came up with
- 02:56
a way that can help Newton's second law of motion
- 02:59
tells us that if an unbalanced force is applied to
- 03:02
an object that object will experience acceleration Will this law
- 03:07
boils down one simple equation That equation says that the
- 03:10
force equals mass times acceleration We can tinker around with
- 03:14
this equation to show just how force and mo mentum
- 03:17
get along Alright now buckle up This might be a
- 03:20
bumpy ride Like we said we've got one of newton's
- 03:23
greatest hits Force equals mass times acceleration All right well
- 03:28
what is acceleration Acceleration is the change in velocity over
- 03:32
the change in time And get that little triangle there
- 03:34
Delta means change in whatever So let's get rid of
- 03:38
a and put this thing into our force equation instead
- 03:41
Okay now how do we calculate change in velocity It's
- 03:45
Not too hard We just subtract the initial velocity from
- 03:48
the final velocity so we can add that into our
- 03:50
equation too So now our equation for force looks like
- 03:54
this force equals mass times final velocity minus initial velocity
- 03:58
over the change in time Kick our algebra skills into
- 04:01
another gear and use the distributive property for that parent
- 04:04
medical Just in case you're having a bad math day
- 04:07
which hey happens to the best of us The distributive
- 04:09
property means that when we have a parenthetical where addition
- 04:12
or subtraction is being done and we're multiplying the result
- 04:15
by something outside the parentheses were gonna multiply that outside
- 04:19
term by each of the terms inside and then ditch
- 04:21
the parentheses altogether So instead of mass times the result
- 04:28
of final velocity minus initial velocity we can change it
- 04:31
to mass times final velocity minus mass times initial velocity
- 04:36
got all that so we're distributing the mass within the
- 04:38
parent medical Okay great fun little math trick but what's
- 04:41
the point Well we have mass multiplied by velocity In
- 04:45
fact we have that twice And what is mass times
- 04:49
velocity It's momenta More mojo more technically speaking So now
- 04:53
we can swap out the m v stuff and put
- 04:55
in momentum And instead of just saying final momenta minus
- 04:59
initial moment and we can call it the change in
- 05:02
mo mentum so now we have a whole new equation
- 05:05
for force to go along with the old school f
- 05:07
equals m a force equals the change in mo mentum
- 05:10
over the change in time and this new equation will
- 05:13
definitely come in handy But we can also rearrange the
- 05:16
new equation assault for the change in momentum Change of
- 05:19
momentum equals force times change in time I don't let
- 05:23
anyone tell you that math and physics aren't creative it's
- 05:27
like people who don't think baseball's creative sometimes you gotta
- 05:30
find a new way to avoid getting tagged out like
- 05:33
that right Well it's the same in science Creativity is
- 05:35
huge thing way have to figure out ways to get
- 05:37
from point a to point Q You can't just sling
- 05:40
the alphabet song under our breath to figure out how
- 05:42
to get there either But the other important thing is
- 05:45
this change in momentum right here Well changing mo mentum
- 05:49
is important because it happens all the time Momentum is
- 05:52
changing everywhere You look okay If you're not looking at
- 05:55
your cat sleeping in the sun where it maybe not
- 05:57
But you might look out your window and see car
- 06:00
slowing down at a stop sign or birds picking up
- 06:03
momentum as they fly off three brands or might see
- 06:06
the left fielder's momentous change very suddenly when he runs
- 06:09
into the shortstop there Changing mo mentum is so important
- 06:13
that it has its own names called impulse has its
- 06:16
own symbol to jay Well you know impulse starts with
- 06:20
a j jj impulse like that How you remember it
- 06:24
Look these symbols are always gonna make sense Just roll
- 06:26
with impulse is the measure of force applied over time
- 06:30
so it makes sense of units for impulse are newton
- 06:32
seconds or to break it down to base units Units
- 06:35
for impulse are kilogram meters per second just like mo
- 06:39
mentum Yeah because you know it is mo mentum or
- 06:42
at least the change in mo mentum And because impulses
- 06:45
force applied over time we can slap it onto a
- 06:47
graph The y axis is the force in the x
- 06:50
axis is the time like you might have seen on
- 06:53
other graphs Such a velocity versus time Here's graph for
- 06:56
a constant force flight over specific amount of time Let's
- 06:59
look at all this green area right here under the
- 07:02
line Don't get too excited This crap isn't going to
- 07:04
reveal the meaning of life Where is money python when
- 07:07
you need him it's just a rectangle And like any
- 07:09
other rectangle we can find its area with a simple
- 07:12
formula Yeah Base times height Remember that from like third
- 07:15
grade Well what is the height represent in this green
- 07:17
shape That would be force And the base is time
- 07:22
We'll force times Time is impulse So the area under
- 07:26
the line on our graph equals the total impulse we
- 07:29
knew Geometry class Would come in handy someday All right
- 07:32
Well what if we don't have constant force That's Harder
- 07:36
Well here's a graph for force that decreases at a
- 07:38
constant rate Same deal We find the area of everything
- 07:43
under the line and here we just use the formula
- 07:46
for the area of a right triangle Eight times be
- 07:48
divided by two Well anytime we apply a net force
- 07:51
to an object over any span of time the objects
- 07:53
acceleration will change anytime acceleration changes Velocity will change in
- 07:58
anytime velocity changes Mo mentum will change All of these
- 08:02
things are our separate but related to each other And
- 08:05
in the real world forces pretty much always applied over
- 08:08
a span of time That span might be tiny like
- 08:11
when a baseball hits a fast the ball in the
- 08:14
bat might only be in contact for a millisecond but
- 08:17
that still counts is a time span in physics but
- 08:20
most time spans air a lot longer than that Like
- 08:22
if we floor the gas pedal for five seconds in
- 08:25
our car or even when my feet hit the ground
- 08:28
is i round second base and it applies to negative
- 08:31
acceleration to like When our center fielder runs into a
- 08:33
wall trying to make it a catch In fact in
- 08:36
our impulse equation the force has a specific name The
- 08:40
force of impact and the relationship between changing mo mentum
- 08:44
in time determines just how hard that impact will be
- 08:48
In fact what makes something soft is completely linked to
- 08:51
changing momentum Let's look back at our center fielder here
- 08:55
Well you know he's getting to know the wall there
- 08:58
likes a great defender but he's going to get hurt
- 09:00
if he keeps on doing that or have to move
- 09:02
to game of thrones and try something with white walker
- 09:04
is doing that thing Yeah all right Well the wall
- 09:07
has a little padding to soften the blow but trust
- 09:09
me it doesn't feel too good Let's Say my kind
- 09:12
of law Save nine meters a second right before he
- 09:14
hits the wall and he has a mass of ninety
- 09:16
kilograms So right before he makes impact his momentum is
- 09:19
eight hundred ten kilogram meters per second What's his momentum
- 09:23
after he hits the wall Really kind of bounces off
- 09:26
of it So there's negative momentum here Walk it off
- 09:30
mike But there Will be a point in this crash
- 09:33
where his velocity reaches zero meters A second and that's
- 09:37
what we're looking for Shmoop so the change in momentum
- 09:46
will be negative Eight hundred ten kilogram meters per second
- 09:50
and let's say it takes a tenth of a second
- 09:52
for this change to be complete So what's the force
- 09:55
of the impact well we just rearrange our impulse equation
- 09:58
to solve for force before sequels impulse divided by time
- 10:02
Oh and we're not i'm gonna worry about having a
- 10:04
negative momentum We'll just use the absolute value Eight nine
- 10:07
and ten kilogram meters per second Invited by point One
- 10:09
seconds gives us a force of eighty one hundred newton's
- 10:12
out No wonder mike still down for the count after
- 10:14
seeing that nasty collision the grounds crew takes pity on
- 10:16
poor mike They cover the outfield wall with a few
- 10:19
layers of bubble wrap because bubble wrap sauce that makes
- 10:22
a change in momentum take a longer amount of time
- 10:24
So now instead of going from full speed to no
- 10:26
speeding point one seconds it'll taking half a second Well
- 10:30
how does that affect the force of the impact Wow
- 10:33
reduces it to one fifth of what it was Well
- 10:36
the new forces sixteen hundred twenty newtons which might not
- 10:39
feel great but it's a lot less likely to put
- 10:41
you on the permanent disabled list but this is why
- 10:44
most safety features in your car are meant to give
- 10:47
your moment and more time to reach zero that's what
- 10:50
airbags do people and crumple zones crumple zones air part
- 10:54
of your car that our mental collapse on impact by
- 10:57
collapsing they're distributing the mo mentum change in a crash
- 11:01
over a longer period of time than a rigid structure
- 11:04
would see knowing newtonian physics can help save lives And
- 11:08
just in case you want to prove it for yourself
- 11:09
go stand on your bed and then fall over on
- 11:12
your mattress kind of fun right now Do that on
- 11:14
the floor a lot less fun right Don't actually do
- 11:17
this by the way our lawyers just made us say
- 11:19
that Sorry Consider it more of a thought Experiment people
- 11:21
Physics is great but not worth breaking ribs over All
- 11:24
right well just remember even though the real world situations
- 11:27
are more complicated than ideal closed systems we still have
- 11:30
the tools to make sense of them The more equations
- 11:32
we know the more we're able to mess around with
- 11:34
them to make them do What we want him to
- 11:35
do so don't be afraid to breaking equation down to
- 11:38
its components and then build those back up in different
- 11:40
ways And don't let all this force of impact stuff
- 11:43
scare you too much Sure it can be a mildly
- 11:46
terrifying thing to think about a big change in mo
- 11:48
mentum over a super short period of time But we
- 11:50
can do things to slow that impact down Like you
- 11:53
know when i lay down a bunt i'm increasing the
- 11:56
time that force is applied to work in my favor
- 11:59
And hey maybe instead of always trying to hit a
- 12:02
home run i'll see if they have any of that
- 12:03
bubble wrap The left over there Yeah they'll never see 00:12:06.739 --> [endTime] this one coming
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