- Good morning.
Bo, could you please read the problem?
And Bobby, could you please translate?
♫ Flipping Physics ♫
- You apply a horizontal force of 2.0 Newtons to
a book with a mass of 0.674 kilograms.
- Please stop.
Force applied equals 2.0 Newtons and is horizontal.
And the mass of the book is 0.674 kilograms.
- Bo, could you please continue?
- The values for the coefficients of friction
between the book and the incline are.
What is the name of that symbol?
- It's called mu, so mu s equals 0.27
and mu k equals 0.24.
- Thanks.
- You're welcome.
- Bo?
- Part a, does the book move?
And part b, what is the acceleration of the book?
- Part a, move equals question mark,
and part b, acceleration equals question mark.
- Billy, please remind me what are my five steps
to help solve any free body diagram problem?
- One, draw the free body diagram.
Two, break forces into components.
Three, redraw the free body diagram.
Four, sum the forces and five, sum the forces again
in a direction perpendicular to the one in step four.
- [Mr. P] Very nice.
We've actually had this same free body diagram
several times in a row now, so I will draw it this time.
- Do y'all really think he would
make the answer to part b zero?
I can pretty much guarantee you, the book moves.
- Bo, you may think that.
However, never underestimate the
Machiavellian stratagems of Mr. P.
(dramatic music)
- I, I don't get it.
- The force applied is to the right, the force of
gravity is down, and the force normal is up,
and the force of friction is to the left.
Now, I have not identified whether
it's static or kinetic friction,
because we don't know if the book is moving or not.
Step two, break forces into components.
Billy, could you please tell me which
forces need to be broken into components?
- Uh, I don't think any of them need
to be resolved into components.
- Right, all the forces are either
directly in the x or y direction.
- And because we don't need to break
any forces into components, we don't need
to do step three, redraw the free body diagram.
So Bobby, could you please do step four?
- Uh, step four, sum the forces.
Let's sum the forces in the y direction.
The net force in the y direction equals the force normal
minus the force of gravity, which then equals
mass times acceleration in the y direction.
We know the acceleration in the
y direction equals zero, so.
- [Mr. P] Hold up, how do we know the
acceleration in the y direction is equal to zero?
We don't even know if the book is moving or not.
- Because when the...
- [Mr. P] Bo, that's if.
- If the book moves, it will move in the
x direction and not the y direction.
Therefore, the acceleration of the y direction will be zero.
- Bobby, please continue.
- Then, we can add the force of gravity to both sides,
to give us the force normal equals the force of gravity.
And the equation for the force of gravity
is mass times the acceleration due to gravity.
We know the mass of the book and the acceleration
due to gravity, so we can plug in numbers.
The mass of the book is...
- [Mr.P] Actually, let's not use numbers yet.
Instead, let's put the equation into our equation holster.
Please.
- Equation holster!
- Billy, could you please do step five?
Could you sum the forces again?
- The net force in the x direction equals the force applied
minus the force of friction, which then equals
mass times acceleration in the x direction.
However, we don't know what type of
friction and we don't know the acceleration so.
I don't know what to do from here.
- At this point, we are trying to determine if the book
moves or not, so let's substitute in for the
force of friction the equation for the maximum
force of static friction and see what happens.
- Okay, and then we can substitute in the
coefficient of static friction times the force normal
for the force of static friction maximum.
Uh, oh, and now from our equation holster,
we can substitute in mass times the acceleration
due to gravity for the force normal.
At this point the only variable we don't know
is the acceleration in the x direction.
Do we substitute in numbers now?
- Yes, now we substitute in numbers.
- Then the force applied is two Newtons,
minus the coefficient of static friction, which is 0.27,
times the mass, which is 0.674 kilograms,
times the acceleration due to gravity,
which is 9.81 meters per second squared.
Which then equals 0.674 times the
acceleration in the x direction.
And 0.27 times 0.674
times 9.81 is 1.7852.
Uh ... However I don't know what else to do with this.
- Believe it or not, this equation shows
us if the book is moving or not.
Bo, how?
- Well.
Two is the force applied
and 1.7852 Newtons is the maximum force of static friction.
So, because the force applied is greater
than the maximum force of static friction,
the book moves.
- Bo, I agree with that in this particular case.
However, I prefer to look at it in a more general sense.
Because the net force in the x direction is positive,
the book will accelerate to the right.
If the net force in the x direction were negative,
that would not mean that the book accelerates to the left.
It would mean, in this particular case, that the force
applied was less than the maximum force of
static friction, and therefore the book does not move.
- Okay, I got it.
If the net force on an object is positive,
we know the object moves.
- [Mr. P] Actually Billy, that's not quite correct.
It's true in this particular case,
but think about it this way.
If we change the direction of the force applied,
then the force of static friction would be in the
positive direction, and the net force would actually
need to be negative in order to cause the book to move.
So in a more general sense, the net force
needs to be opposite the direction of
the force of friction in order for the book to move.
- The direction of the net force needs to be opposite the
direction of the force of friction for the object to move.
- Okay, uh. Bobby, could you please answer part b,
what is the acceleration of the book?
- We have an equation right there for
acceleration, so let's solve that.
Divide both sides by 0.674.
And we get acceleration equals two minus 1.7852,
divided by 0.674.
And that gives us 0.31866, or with two sig figs,
0.32 meters per second squared.
- And unfortunately, this is incorrect.
I need to know why this is incorrect.
- The book is moving now.
- Right, so it's not static friction anymore.
- We need to use the coefficient
of kinetic friction instead.
- Because the equations for the force of static
friction maximum, and the force
of kinetic friction are so similar,
we simply have the coefficient of kinetic friction
instead of the coefficient of static friction.
The two equations end up being almost identical.
Again it's simply the difference
between having a coefficient of static friction
and a coefficient of kinetic friction.
And the acceleration of the book in the x
direction is 0.61 meters per second squared.
And not 0.32 meters per second squared.
Because when an object is moving, when an object is
sliding relative to a surface, we need to use
kinetic friction and not static friction.
Thank you very much for learning with me today.
I enjoyed learning with you.