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Welcome back, we just finished this problem with the police and the
inclined plane, and I just wanted to do one final thing on this problem just because I think it's
interesting, and then we can move on to what seems like a pretty fun problem
so the last thing I want to figure out is we figured out this 20kg
actually the whole system will accelerate up and to the right at 4.13 meters per second squared
and then the second part of this question is, what is the tension, what is the tension in this rope or this wire
and at first you might say oh this is complicated you know, this thing isn't static anymore
the thing is actually accelerating, how do I do it? Well this is how you think about it. Just pick one
part of the system. Let's say that all we could see was this 20kg mass
right? so let's say all we could see was this 20kg mass
and we know it's suspended from a wire. And we also know that this 20kg mass
is not accelerating as fast as it would if the wire wasn't there,
it's accelerating only at 4.13 meters/second, if the wire wasn't there
it'd be accelerating at 9.8 meters/second, just the acceleration of gravity. So the wire must be exerting
some upward force on the object, and that is the force of tension
that is what's slowing, that's what's moderating its acceleration
from being 9.8 meters per second squared to being 4.13 meters
per second squared. So, essentially, what is the net force on this object? on just
this object? well the net force is, and you can ignore what I said before about
the net force in all the other places, but we know that the object
so, we know that the object is accelerating downwards, well we know it's 20kg
that's its mass, and we know that it's accelerating downwards at 4.13 meters per second squared
so the net force, 20 times
see... times 20
is 82... let's just say 83 Newtons
83 Newtons down. We know that the net force is 83 Newtons down. We also know that the tension force
the Tension force plus the force of gravity, and what's the force
of gravity? the force of gravity is just the weight of the object, so the force of tension which
goes up, plus the force of gravity, is equal to
the net force. And the way I set this up tension is going to be a negative number
just because I'm saying positive numbers are downwards, so a negative
number would be upwards. So tension would be what what is 83
what is 83 minus 196
minus 196 is equal to
-113 Newtons, and the only reason why I got a negative number is because I used
positive numbers for downwards. So -113N downwards, which is the same thing
as 113 Newtons upwards, and so that is the tension
in the rope. And you could have done the same thing on this side of the problem, although it would have been
well... yeah, you could have done the exact same thing on this side of the problem. You would have said
well what would it have accelerated naturally if there wasn't some force of tension on this rope
going backwards. And then you say oh well we know it would have gone in this direction
with some acceleration but instead it's going in the other direction, so you use that
you figure out the net force and then you say the tension plus all of these forces have
to equal the net force and then you should solve for the tension, and it would be the same
tension. Now we will do a
fun and somewhat simple but maybe
instructive problem. So I have a pie
this is the pie
this is the pie, this is paralell, let's see, and I have my hand
you can tell that
you can tell that my destiny
was really to be a great artist. This is my hand, and I'm holding up
a pie, and I'm looking to smash this pie
into this individual's face
actually I was a
I was the newspaper cartoonist in high school
so I have some minor... but anyway, let's make it a bald
man. Anyway I shouldn't be focusing on the drawing
hey let's make him more... let's have... see he has a mustache
anyway, I am looking to throw this pie into this guy's face
and the problem is I need to figure out how fast do I need to
accelerate this pie for it to not fall down, right? because what's happening?
well there's a force of gravity on this pie, there's a force of gravity on this pie
and if I don't accelerate it fast enough, it's just going to slide down and I'll
never be able to... it'll never reach the guy's face, so I don't want this pie
to slide down at all. How far-fast do you have to push on it?
we know that the coefficient of friction... well you don't know this, but I know that the coefficient
of friction between my hand and the pie
the coefficient of friction is equal to
0.8, so given that, how fast do I have to accelerate it?
well let's see what's happening. So we have the force
of gravity pulling down. So let's say that the mass of the pie is
m, m equals mass
so what is the force of gravity pulling down on the pie?
well the force of gravity is just equal to m times 9.8
right? the force of gravity is equal to
m times 9.8. In order for this pie to not move down
what do we know about the net forces on that pie?
well we know that the net forces on that pie have to be zero
so what would be the offsetting force? well it would be force of friction
so we have a force of friction acting upwards, right? because the force of friction
always acts opposite to the direction that the thing would move otherwise
so essentially our force of friction, our force of friction
has to be greater than, roughly, greater
than or equal to, because if it's greater then it's not like the pie is going to move up. Friction
by itself will never move something, it'll just keep something from being moved
but let's just figure out the minimum, I won't do the whole inequalities. The force of friction
has to be equal, similarly, to 9.8
times the mass of the pie
so if the coefficient of friction is 0.8
what is the force that I have to apply?
well, the force I have to apply in this case is going to be the normal force, right?
it's normal to the bottom of the
pie, right? I am like the, my hand is now like the
surface of the ramp. So this is the normal force
and we know that the force of friction is equal to the coefficient of friction
times the normal force, I'm going to switch colors because this getting monotonous
so and the force of friction we know has to be 9.8
times the mass, so 9.8 meters per second times
the mass, 9.8m is the force of friction, and that has to
equal the coefficient of friction times the normal force. Remember the normal force is
the force that I'm pushing the pie with, and we know that
this is 0.8, so we have 9.8 times the mass
not meters, that's the mass, is equal to 0.8
times the normal force, and then so you have the normal
force is equal to 9.8
times the mass, divided by .8
what's 9.8 divided by .8?
9.8 divided by .8 is equal to
12.25
so the normal force I have to apply is 12.25
times the mass, so that's the force I am
applying, it's times the mass, we don't know the mass of the pie. So how fast am I accelerating the pie?
well, force is equal to mass times acceleration
this is the force, 12.25m
that's the force, is equal to the mass
times the acceleration of the pie, and it's the same pie that we're dealing with
all times, it's still m, and you can take out m from both sides of the equation
so the acceleration, the rate at which I have to change the velocity
or the acceleration that I have to apply to the pie is
12.25
meters per second squared, and so actually I have to
apply more than one G, right? because
G is the force of gravity, and the gravity accelerates something at
9.8 meters per second squared
so I have to push and accelerate the pie
at 12.25 meters per second squared, so it's something a little over
1G, and in order for that pie to not fall and in order for my normal force
to provide a force of friction, so that the pie can reach this
bald man's face. I will see you in the next video