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Physics: Calculating the Force of Friction 9 Views
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Description:
In this video, we'll calculate the force of friction - both static and kinetic. And we'll answer that age-old question: fact or friction?
Transcript
- 00:00
Shmoop! Calculating the force, of friction. The force. The reason for that burning
- 00:08
sensation. Yeah, just moving right on from that, catching up on friction.
- 00:13
[mumbling]
- 00:22
[mumbling]
- 00:27
All right,
Full Transcript
- 00:32
here we go. Well you know sliding isn't as easy as
- 00:35
it seems. Sure it might look like a fun time,
- 00:38
kicking up dirt, as you slide into second base. But you have to make sure you know
- 00:43
when to start your slide, which means you have to think about how much friction
- 00:47
you're going to encounter, otherwise you know, things could go badly. [man on baseball field]
- 00:51
Well friction is one of those things we just know. We don't really think about it,
- 00:55
but it's such a part of our everyday life, that we have an intuitive
- 00:58
understanding of it, at least on some level. But as we've seen before, our
- 01:02
intuitive understanding doesn't necessarily match up with what's
- 01:05
happening, in terms of physics. So while you intuitively know how far you can
- 01:10
slide across the floor in your socks, without crashing into a wall like Tom
- 01:14
Cruise. Well you probably aren't thinking about the coefficient of friction, as you
- 01:18
glide along there. Well the physics definition of friction, is the force
- 01:22
that's exerted by two objects as they rub, or slide across each other.
- 01:28
Alright well friction occurs, because there's no such thing as a perfectly [man in glass store]
- 01:32
smooth surface. A piece of glass might look and feel perfectly smooth to us. But
- 01:37
if you look close enough, under a microscope, you'll see all kinds of nooks
- 01:41
and crannies on the surface. Rub your finger across a piece of sandpaper and
- 01:46
you'll feel the rough surface slowing your finger down. There's no material
- 01:50
that's perfectly smooth, at least not that we've discovered yet. But hey, if you
- 01:54
can invent a frictionless material, you'll probably become a gazillionaire [man sitting in private library with bags of money]
- 01:58
and be able to buy your own baseball team. So you know, go for it. Alright,
- 02:02
well the second factor, that determines the strength of friction, is how much
- 02:06
force is pressing the two objects together. Rub your finger down the
- 02:11
surface of your table, or you know baseball bat, if you have one lying
- 02:15
around. Just barely graze your finger across, pretty easy right? Now really mash
- 02:21
your finger down on to the table and drag it across. Well it takes a lot more [man with baseball bat]
- 02:24
effort to move your finger, when it's pressed hard against the table. Well
- 02:29
here's the mathematical formula to figure out friction. This equation says
- 02:33
that the force of friction, that F there, equals the coefficient of friction, which
- 02:39
is that mue symbol there, times the normal force, which is what the big n thingy
- 02:44
there, stands for. Well the normal force, is the force that's pressing the two
- 02:48
objects together. That's normal. The coefficient of friction is, kind of
- 02:52
like a measurement of how smooth the two object surfaces are. If the objects move
- 02:58
across each other smoothly, like two pieces of telescope reflector mirror. [man in workshop]
- 03:02
Well the coefficient will be low. If they really dig into each other, like two
- 03:07
pieces of sandpaper, or you know something rubbing the barnacles on the
- 03:11
bottom of a boat. Well the number will be really high. The coefficient of friction
- 03:15
is a value, that can only be determined experimentally. We can't just look at two
- 03:20
materials and put a number on there coefficient of friction. We have to
- 03:24
actually rub two materials across each other, to see how much friction they [scientist preforming an experiment]
- 03:28
generate. We'll get deeper into that coefficient thing in a minute. Well there
- 03:32
are two kinds of friction, static and kinetic. Static friction, is the force
- 03:37
between two objects, when they're in contact. But not moving. When they're
- 03:41
touching, you know just sitting there. Kind of like a congressman. Kinetic
- 03:45
friction, is the force of friction, between two objects that are sliding
- 03:49
across each other. Kinetic friction is almost always weaker
- 03:52
than static friction and you've probably had experience with that, if you've ever
- 03:56
pushed a car, you know it takes more effort to get it moving, than it does to [two men pushing car]
- 04:01
keep it moving. Of course it takes even less effort to remember to fill up the
- 04:05
gas tank in the first place, but that's topic for neurology, not physics and good
- 04:10
luck with that. Why is static friction stronger than
- 04:13
kinetic friction? Well when two objects are stationary, those nooks and cranny's
- 04:18
we talked about earlier, have a chance to really get in close with each other.
- 04:22
They're kind of hooked together, but when they're sliding, they don't
- 04:26
have the chance to cozy up so much, or so deeply. So it's easier to keep things [car rolling on pavement]
- 04:32
just kind of bump and moving along there. Let's get back that coefficient of
- 04:35
friction thing. Well like we said before, the only way to find the coefficient is
- 04:39
to actually rub the two things together. Luckily for us, some smart scientists
- 04:43
have been rubbing stuff together for a long time. Which might sound
- 04:47
inappropriate, but it's not. This is a g-rated video people. They've already
- 04:51
discovered the coefficients of friction for a bunch of materials and you can
- 04:55
find some of them right here. Alright well the coefficient of friction, is a [list of coefficients]
- 04:58
ratio of the force of friction, between two objects and the normal force pushing
- 05:05
them together. In most cases it's a number, between 1 and 0, because in most
- 05:09
cases, the force of friction is less than the normal force.
- 05:13
Now think about when you pressed your finger hard against the table and then
- 05:17
slid your finger across it. The force you used to slide your finger, was less than [man rubbing his finger on bat]
- 05:23
the force you were using to press down. Well there are some materials that have
- 05:27
a coefficient that's higher than one. Like certain kinds of rubber, for example.
- 05:31
Like the rubber hooks on to the other piece of rubber and the hooking this
- 05:35
creates incredible friction and it's like very hard to slide it, got it?
- 05:39
The coefficient can depend on a lot of factors though. The coefficient of
- 05:42
static friction, is almost always higher than the coefficient of kinetic friction.
- 05:47
Is the surface wet, or dry. Well ice is slippery enough, when it's below freezing
- 05:52
outside. But what happens when that ice starts to melt? Well that's a recipe for [woman slipped on icey sidewalk]
- 05:57
a broken tailbone. And when you're trying to stretch that single, into a double, it
- 06:02
can seem like the coefficient of friction between you and the infield
- 06:06
dirt is like somewhere around 60. So let's have some fun with friction.
- 06:10
Let's say I struck out, just pretending here and I'm dragging my bat onlong the
- 06:16
ground, as I head to the dugout. Hanging my head in shame. The bat has a
- 06:20
mass of, 0.88 kilograms and takes 6.7 Newton's of force, to get it
- 06:24
moving along the grass and 4.2 Newtons to keep it in motion at a constant [man dragging bat]
- 06:29
velocity. Well, what are the two coefficients of friction, between the bat
- 06:33
and the baseball field? Well, okay the force needed to get that bat moving is
- 06:38
going to relate to static friction. After what was happening to the bat before we
- 06:42
started dragging it. Well nothing, nothing at all. Nothing was moving it and anytime
- 06:47
we have an object at rest, we know we have a first law situation. Where the [baseball player talking]
- 06:51
forces are balanced. Newton's first law states that, objects at rest, tend to stay
- 06:57
at rest, objects in motion, tend to stay at motion. Well the only way motion
- 07:01
changes, is if a force is applied to it that is out of balance with any other
- 07:06
forces affecting it. Something that's just resting on the grass isn't
- 07:10
experiencing any imbalance of force. And the force to keep it moving is going to
- 07:15
relate to kinetic friction. Since we have constant velocity when the bat is moving,
- 07:20
we know we have balanced forces, here to. Remember when there's no acceleration,
- 07:25
either positive, or negative. Then we have another case of balanced forces. So let's [equations on chalkboard]
- 07:31
figure out the kinetic coefficient first. Alright, our formula tells us that
- 07:36
friction equals the coefficient, times the normal force. We're trying to find
- 07:40
that, mue thingy, right there. We'll go ahead and make a Freebody diagram for
- 07:45
this. There we go and the square here is our bat and we've got our forces all
- 07:50
lined up. Alright, we know our applied force and we know how to find the
- 07:54
gravitational force. We don't know the force of friction, F sub F and we don't [diagram and equations]
- 07:59
know the normal force, F sub n. So let's rewrite our friction formula, in terms of
- 08:04
our FB D, so we don't get confused. Well F sub F, equals the coefficient, times F sub
- 08:10
n. We know our applied force is 4.2 Newton's. Well since our forces are all
- 08:15
nice and balanced. The force of friction has the same magnitude. Well how about
- 08:19
the normal force? Well it's gonna match the force of gravity and we know how to
- 08:24
find that out. The force of gravity equals, mass times the acceleration of [formulas on chalkboard]
- 08:28
gravity. Well the mass is 0.88 kilograms and gravity is as reliable as it gets
- 08:33
with an acceleration of 9.8 meters per second squared. So the bad has a weight
- 08:39
of 8.6 Newtons and the magnitude of the normal force is exactly the same. Now
- 08:45
that we have the numbers, we can find the coefficient. Well 4.2 Newton's equals, the
- 08:50
coefficient of friction, times 8.6 Newtons.
- 08:53
To isolate coefficient, we divide each side by 8.6 newtons and that tells us
- 08:58
that the coefficient of kinetic friction equals 0.49. [equations on chalkboard]
- 09:02
That'll be mue sub K, so we don't get it all mixed up with static friction. Well
- 09:07
to solve for that static coefficient, we just have to swap in the right force. Our
- 09:11
equations already set up for us, it took 6.7 newtons to get the bat moving. We
- 09:16
divide both sides of the equation by 8.6 Newton's. Giving us a static coefficient
- 09:21
of 0.7 8 and that looks about right. The static coefficient should be higher, than
- 09:26
the kinetic coefficient, in most cases. Right? But I'm mad about striking out. I
- 09:31
want to get a hit and I'm so mad, I'll hit pretty much anything. Like say the[baseball player in locker room]
- 09:37
shelf that the watercooler is sitting on. Great so now I've done it, I've broke
- 09:42
the shelf on one side, creating an incline. The watercooler has a mass of
- 09:46
6.6 kilograms and the incline has an angle of 38 degrees. Well if the water
- 09:50
cooler and the shelf have a coefficient of friction of 0.48. How fast will the[watercooler on its side with equations]
- 09:56
water cooler accelerate? Okay, let's figure this thing out, before the manager
- 10:00
comes here to yell at me. Here's a force diagram of this mess. Which looks pretty
- 10:06
familiar, to what stuff we've worked on in previous lessons, right? To make things
- 10:11
easier on ourselves, let's tilt the diagram, so the incline is on the x-axis.
- 10:15
There that's better. Only one diagonal line to deal with. We'll go ahead and add
- 10:19
in the component vectors for gravity in the X and y directions. Before we go
- 10:24
too far, let's set up our second law equations. Well Newton's second law tells
- 10:28
us, that the sum of all forces along one plane, equals the sum of forces in the [formulas on chalkboard]
- 10:34
positive direction, minus the sum of forces in the negative direction. The sum
- 10:39
of forces on the y axis, equals F sub n, minus F sub G Y and the sum of forces
- 10:46
along the x axis, equals F sub G X, minus F sub F. So let's tackle the Y forces
- 10:52
first. Step one is to put F sub y in terms of F sub G and F sub G, equals mass
- 10:58
times the acceleration of gravity. Well we'll do the math on that one real quick.[equations on chalkboard]
- 11:03
6.6 kilograms, times 9.8 meters per sec
- 11:07
second square, gives us a force of 65 Newtons. Our angle here, at the top of our
- 11:12
component triangle, will match the theta angle, of our incline and we'll need that
- 11:17
to figure out F sub G y. Trigonometry is gonna be our weapon of choice here.
- 11:21
Cosign theta, equals f sub G y, over f sub G. Pop in the numbers and multiply both
- 11:27
sides by F sub G, to solve for F sub G Y. Well F sub G y, equals 51 Newtons. Which [formulas on chalkboard]
- 11:34
means the normal force F sub n, has the same magnitude. Alright, now for
- 11:40
friction. What's our friction formula? Well friction equals the coefficient,
- 11:43
times the normal force. Our coefficient is 0.48 and our normal force is 50 1.2
- 11:50
Newton's. Meaning friction has a force of 25 Newtons, in this case anyway. Write
- 11:55
that down somewhere, we'll need it soon. But first we need to figure out the X [person writing on paper]
- 11:59
component of gravity. We'll use the sign function for that one.
- 12:02
Well sign theta equals, F sub G x, over F sub G. The solving for F sub G X, gives us
- 12:08
a force of 40 Newtons. Yeah, see what we did there. Now we can find the sum of forces,
- 12:13
on the X plane. Well the sum of forces in the X Direction, equals F sub G X, minus F
- 12:18
sub F. Well F sub G X, is 40 Newtons and F sub F is 25 Newtons, giving us a net
- 12:25
force of 15 Newton's. Fantastic, now we have what we need to find the [man in locker room with broken water cooler]
- 12:29
acceleration of this water cooler. Then we can see how fast I'm accelerated back
- 12:35
down to the minors. Well force equals mass, times acceleration. Our force is 15
- 12:40
Newtons and our mass is 6.6 kilograms, we divide each side by the mass to solve
- 12:45
for acceleration. Meaning that cooler is accelerating at 2.3 meters per second
- 12:50
squared. No friction is one of those things that seems simple, until we really [baseball game]
- 12:54
start thinking about it. We've been running into a lot of these things in
- 12:57
physics, but it's always good to get a deeper understanding of how stuff
- 13:00
actually works. Well for one thing, now we know that there are ways to reduce
- 13:04
friction. Like motor oil, which reduces friction in a car's engine. Yeah, if
- 13:09
I want to steal second base, I can just pour motor oil all over myself and [baseball player running]
- 13:14
reduce that coefficient of friction. What could go wrong? Is that legal?
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