Good morning. A while back we had a lesson where I described why I require you to
“Show All Your Work!”. ♪ Flipping Physics ♪
Today let’s look at an example of something students typically want to skip,
however, I require that you write down every time because I require that you “Show All Your Work!”.
A basic example of a book at rest on a level surface with a person applying a force to the
right on the book like this. Bobby, please tell me all the forces acting on the book and their
directions so we can draw the free body diagram. Okay. You are pushing to the right on the book,
so there is a force applied acting to the right on the book.
But, the book is at rest and not accelerating in the x-direction, so there must be a force acting
to the left to keep it from accelerating. It’s a force of friction.
That makes sense. Thanks. There is a force of friction acting to the left. The book has mass,
so it has a force of gravity acting downward on it. Again, the book is not moving down, so there
must be a force acting upward to prevent that. That’s the force normal from the table.
Oh right. Thanks Billy. You’re welcome.
Great. Thank you. We just learned that Newton’s Second Law states that net force equals mass times
acceleration where both force and acceleration are vectors. Bo, please use Newton’s Second
Law in the y-direction on this book while I am applying a force to the right. This
is what I typically call “summing the forces”. Sure. When we sum the forces in the y-direction,
the force normal is up so it is positive, and the force of gravity is down so it is negative.
As you said, net force always equals mass times acceleration,
in this case, because it is the net force in the y-direction,
the acceleration is also in the y-direction. Uh. (The book is at rest.)
Sure. Because the book is not moving in the y-direction and is still not moving in the
y-direction, it is also not accelerating in the y-direction, that means the acceleration in the
y-direction equals zero, and anything times zero equals zero. That means force normal
minus force of gravity equals zero and we can add force of gravity to both sides,
and we get force normal equals force of gravity. Thank you Bo. We could go further in this problem,
however, this is where I want to stop for today because we just showed that, in this situation,
the force normal and force of gravity are equal in magnitude. And, because these same steps will be
repeated many times in many of the problems you solve which include free body diagrams,
many of you want to assume that the force normal and force of gravity are always equal in magnitude
and you want to skip writing down the entire equation which precedes that equation. However,
please realize that force normal and force of gravity are NOT ALWAYS equal in magnitude.
Force normal and force of gravity are NOT ALWAYS equal in magnitude. Got it.
And, if you get into the habit of always thinking your way through and actually writing out the
equations, you will understand when force normal and force of gravity are not equal in magnitude.
There are many, many situations where they are not equal, however, it takes a bit of time in
introductory physics to get to most of those situations. Here are some examples: Bo in an
accelerating elevator. A book on an incline. A book being held against a vertical wall. A car
going over a hill. And a painter on a scaffold. (Uh, mr.p?)
Yes, Dr. Jisonna? There is a simple example
you can show with that book where the force normal and force of gravity are not equal in magnitude.
(I agree. Would you like to tell us?) Sure! If instead of pushing to the right
on the book, you push down on the book, you’ll increase the normal force acting on the book.
That is absolutely true. And easy to demonstrate. Billy, please tell
me how this changes the free body diagram. (Certainly! Well, the force of gravity is
still straight down. The force you are applying is also straight down.) And the force normal is still
straight up only, you said the force normal is larger now, so that arrow should be a bit longer.
Oh, yeah. I see. Now the net force in the y-direction equals force normal minus force
of gravity minus force applied. The book is still at rest, so the acceleration of the book
in the y-direction is still zero. That means the force normal equals the force of gravity plus the
force applied, not just the force of gravity. And that means the length of the force normal
arrow should be equal to the length of the force of gravity arrow plus the length of
the force applied arrow. That is cool!
Yeah! Yeah, you could also put the book on a force
platform to demonstrate that the magnitude normal force increases as you push down on the book.
{Sneeze} Bless you!
Bless you! Thanks.
COVID. Good point. Believe it or not,
I actually have a force platform. So, I can take the force platform and place it right here. And,
when I put the book on the force platform, the reading on the force platform is 38 newtons. That
means, before I push on it, the magnitude of the force normal measured by the force platform equals
38 newtons. Which is the same value right now as the force of gravity acting on the book. And,
when I push down on the book, the value of the force normal increases as y’all proved it would.
(The force platform measures the force normal and not the force of gravity?)
Oh, yeah, I’m not going to go into detail about that today, we are going to go over that in a
future lesson. Here I just want you to recognize that, when we add a force applied downward on the
book, the force normal increases in value. Sure. I can be patient.
Good. Thanks for your help Dr. Jisonna. You’re welcome mr.p.
Okay, I think that’s all I (mr.p?)
Yes, Mr. Hansen? It’s time for, what you like to call,
“Letting go of numbers dependency”, right? Actually, not quite.
But? That’s the same free body diagram we plan to use for demonstrating “numbers dependency”.
Actually, it’s not quite the same free body diagram and not quite the same situation. And
Bo, has not ridden in the elevator yet. He hasn’t? I just saw the lesson.
Right, the Flipping Physics Universe timeline doesn’t quite match that of
the Earth’s. It can get confusing at times. I’ll just let you know when it’s your turn.
Okay. Just know I’m ready. I know.
I’m confused. Uh.
What elevator? Okay. That’s it for today.
Thank you very much for learning with me today, I enjoy learning with you.