- Good morning.
Today we're going to find the net force of my three brothers
fighting over the stuffed turtle
my grandmother made for my brother Ken.
- Hey Guys.
- Hey Bo.
- Hi Bo.
♫ Flipping Physics ♫
- [mr.p] Ken, what is the name of your stuffed turtle?
- Turtle.
- Really, Ken?
You named your stuffed turtle, Turtle? (chuckles)
- I was one year old.
- Okay, sure.
Bobby, could you please read the problem.
- [Bobby] Three brothers Ken, Jim and Chris
all want Ken's stuffed turtle.
Each is pulling with a horizontal force.
If Ken pulls Eastward with 270 Newtons,
Jim pulls Southward with 130 Newtons
and Chris pulls with 260 Newtons at an angle of
33 degrees west of north,
what is the net force caused
by the three brothers on the stuffed turtle?
- Okay, let's see what this looks like.
- Guys.
(dramatic music)
- And now Bo, could you please tell me the givens
and what we're solving for?
- [Bo] The force of Ken equals 270 Newtons east;
the force of Jim equals 130 Newtons south;
the force of Chris equals 260 Newtons
at an angle of 33 degrees west of north.
And, net force equals question mark.
- Notice the subtlety here with the force of Ken,
it is 270 Newtons east,
not 270 northeast with no dimensions.
So please be careful of that.
Now, Bobby, this is a problem that involves forces
so what should we do next?
- [Bobby] We need to draw the free body diagram.
- Absolutely. We need to draw the free body diagram.
The force of Chris is 260 Newtons
at an angle of 33 degrees west of north.
The force of Ken is 270 Newtons east,
and the force of Jim is 130 Newtons south.
Remember the length of the arrows is proportional
to the magnitudes of the vectors,
which is why the force of Jim arrow is the shortest,
and the force of Ken and Chris arrows are almost
the same length.
Be aware that there actually is a force of gravity
acting on turtle,
however it is only 1.4 Newtons
and we're considering it to be negligible for this problem.
Which means it is so small we can disregard it
with very little error.
Now we need to find the net force
caused by my three brothers.
Billy, what do we need to do before
we can determine the net force?
- [Billy] I, I don't know, can't we just
add 270 plus 130 plus 260
to get 660 Newtons?
- [Bobby] If force were a scalar we cloud do that
but force is a vector, not a scalar.
- [Bo] Yup.
We need to break the force of Chris into its components.
- [Billy] Yea, that's right.
But we don't need to break the force of Ken
or the force of Jim into their components,
because those two forces are already
in the x or y direction.
- Great. Now Billy could you please find
the components of the force of Chris?
- [Billy] Uh, okay, uhm
cosine theta equals adjacent over hypothenuse,
and adjacent theta is the force of Chris in the y direction,
and the hypothenuse is the force of Chris
multiplied by the force of Chris
and we get the force of Chris in the y direction
equals the force of Chris times the cosine of theta,
which is 260 times the cosine of 33 degrees
or 218.054 Newtons.
We can do the same thing with sine, uh,
sine theta equals
opposite over hypothenuse
or the force of Chris in the
x direction divided by the force of Chris.
So then the force of Chris in the x direction
equals the force of Chris times the sine of theta
which is 260 times the sine of 33,
which is 141.606 Newtons.
- Now, this next step of redrawing the free body diagram
is one that I find students often want to skip
to try to save time.
However, fewer mistakes are made when we redraw
the free body diagram.
Because then you can visualize
the rest of the problem easier.
So please, always redraw the free body diagram.
We still have the force of Jim and the force of Ken.
But now instead of having the force of Chris,
we have the components of the force of Chris,
the force of Chris and the x direction
and the force of Chris in the y direction.
Our goal is to figure out the net force
but before we do that
we need to figure out the components of the net force.
Bo, please tell me the forces that are acting on Turtle
in the x direction
and whether they are positive or negative.
- [Bo] The forces in the X direction are
the force of Chris in the x direction which is west
and negative.
And the force of Ken which is to the east and positive.
- And we can substitute in numbers to get negative 141.606
plus 270
is equal to 128.394 Newtons
the net force in the x direction.
Bobby, could you please do the same thing
in the y direction.
- [Bobby] The net force in the y direction equals
the force of Jim which is negative because it's south.
Plus the force of Chris in the y direction which is
positive because it's north
with numbers that's
negative 130 plus
218.054
or 88.054 Newtons.
- Now we can calculate the net force.
Let's draw that triangle.
Notice I have used the angle phi for the net force
and not the angle theta like we use for the force of Chris,
because I don't want to confuse those two angles.
Billy could you please figure out the net force?
- [Billy] Uh, we need to use a Pythagorean theorem
so a squared, plus b squared, equals c squared.
Which is then the net force of the x direction squared
plus the net force of the y direction squared
equals the net force squared.
Uh, taking the square root of the whole equation
gives us the net force equals the square root of
the net force in the x direction squared,
plus the net force in the y direction squared.
Uh, when we substitute in numbers
it is the square root of 128.394 squared
plus the square of 88.054, uhm, and--
- [Bobby] 155.687 or
160 Newtons with two significant digits.
- And there you have it.
The net force is 160 Newtons.
(sighs)
- [Billy] (laughs] Oh, oh yeah, for--
force is a vector.
- [Bo] We need to find the direction.
- [Mr. P] Yep.
Force is a vector.
So we need to find the angle phi for the net force.
Bo, could you please do that?
- [Bo] Sure.
(sighs) tangent of phi equals opposite over adjacent
or the y direction net force divided by
the x direction net force.
Take the inverse tangent and
phi equals the inverse tangent of the y direction net force
divided by the x direction net force
or the inverse tangent of 88.054
divided by 128.394 which is
34.4429
or with two significant digits 34 degrees.
- The net force acting on turtle, with two sig figs,
is 160 Newtons at an angle of 34 degrees north of east.
Thank you Ken, Jim and Chris for being in my video today.
Uhm, yes Bobby?
- [Bobby] If the net force acting on turtle
has a magnitude of 160 Newtons,
shouldn't Turtle accelerate?
- [Bo] Yea.
- [Mr. P] Very good observation, Bobby. You are correct.
Because Turtle's initial velocity is equal to zero
he should accelerate in the direction of the net force
which is 34 degrees north of east.
(rumbling)
(explosion)
However, because Turtle was made by my grandmother
47 years ago,
it seemed appropriate to pantomime those forces
to avoid ripping Turtle apart.
(chuckles)
Thank you very much for learning with me today.
I enjoyed learning, with you.
(jazzy music)
- [mr.p] So you need to be standing so that
kind of in a line (mumbles)
(mumbling)
That's good.
- [Ken] Be nice to me.
If I fall down and break something
and have to go to the hospital it's a long ways.
Be nice to me.
- Turtle.
- [mr.p] Excellent.
(laughter)
- [mr.p] That was awesome. (clapping)
- Be nice to each other.
- [mr.p] Grunt like you mean it.
- (low grunting)
- [mr.p] (laughter) I like it, okay (mumbles).
Give me the look (laughter)
- (laughs) Whatever.
- [Jim] Zoom in on that.