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In this segment, we're gonna learn about what forces
are in play when an arrow like this soars through the air.
Here's a hint.
Don't just look at the arrow.
Check out the bow.
It's a key part of this action.
The moment the archer pulls back the string and releases,
the force from the string sends the arrow soaring.
Let's look at this in slow motion.
Not only is there a forward motion,
check out the backward motion.
As the string is pulled back,
the string exerts force on the arrow.
What's harder to see is that, at the same time,
the arrow exerts force right back on the string.
When the arrow is released,
the bow moves less than the arrow
in the opposite direction, but does accelerate a little.
And the archer is definitely feeling the force.
How much?
Let's figure it out.
You are now seeing Sir Isaac Newton's
Third Law of Motion.
Another way to say it?
So, if object A exerts a force on object B,
object B will exert a force on object A
that is equal in magnitude and opposite in direction.
We know from Newton's second law
that force is equal to mass times acceleration.
We can now see that when we substitute
the second law equation into the third law,
we can analyze our forces acting in more detail.
This may be hard to believe
because it doesn't appear equal at all in this case.
The bow seemed to stand still
while the arrow flew into the air.
But why?
It's all about the mass of the bow
versus the mass of the arrow.
Let's figure out how much the bow will accelerate back
as the arrow is launched forward into the air.
The arrow has a mass of 0.10 kilograms,
with an average rate of acceleration of 1280 meters
per second squared.
The mass of the bow is 4 kilograms.
The bow exerts a force on the arrow
as it is fired in the positive X direction.
According to Newton's third law,
the bow will also experience a force from the arrow
of equal magnitude in the negative X direction.
We see that by substituting in Newton's second law,
the mass of the arrow times the acceleration of the arrow
equals the mass of the bow
times the acceleration of the bow
in the opposite direction.
We can rearrange this equation
to solve for the acceleration of the bow.
The acceleration of the bow equals
negative the mass of the arrow
times the acceleration of the arrow
divided by the mass of the bow.
We can now plug in our values to find the acceleration.
Negative 0.10 kilograms times 1280 meters per second squared
divided by 4 kilograms
equals negative 32.0 meters per second squared.
Or, 32.0 meters per second squared
in the negative direction.
Thus, the bow accelerates backwards
at 32.0 meters per second squared.
If the force of one thing acting on another
is always equal in magnitude yet opposite in direction,
then how does anything ever accelerate?
Even though the two forces are equal in magnitude,
one can accelerate more than the other
because one can have a smaller mass.
Like the arrow when compared to the bow.
The much smaller arrow accelerated
at 1,280 meters per second squared,
while the much larger bow accelerated at a smaller amount.
32.0 meters per second squared.
Okay, let's head for the skies and look at another example.
A sky diver is in a free fall toward Earth.
The Earth is pulling the sky diver with the same force
as the sky diver is pulling on the Earth,
but in the opposite direction.
Even though the forces are the same,
the sky diver is accelerating to the Earth
exponentially faster than the earth is accelerating
toward the sky diver.
Because Earth is so much more massive,
it takes a lot more force to move the Earth
compared to the sky diver.
So the acceleration isn't the same
and neither is the mass.
So each side of the equation is equal,
but the variables on each are bigger or smaller
depending on the mass and acceleration of the objects.
As far as physics goes and following Newton's third law,
the Earth does accelerate toward the sky diver
ever so slightly.
We can sum up this idea into what's called
an action-reaction pair.
Action-reaction pairs show...
As a sky diver jumps from a plane,
the Earth pulls on the sky diver
and the sky diver pulls back on the Earth.
What are some other action-reaction pairs?
When you walk down the sidewalk,
you push on the ground, the ground pushes on you.
A swimmer pushes on the water.
The water pushes back on the swimmer.
A hammer pushes on a nail.
The nail pushes back on the hammer.
At a rocket launch,
the rocket's weight... yes, weight is force...
is pushing on the ground,
and the ground is pushing back on the rocket.
An action-reaction pair.
And on lift-off, inside the rocket engine,
all the combustion gasses are igniting,
pushing on the rocket.
And the rocket is pushing back on the gasses
with a force equal in size, but in the opposite direction.
Another action-reaction pair.
It is this rocket combustion gas action-reaction pair
that will cause lift-off,
as well as the movement of the rocket into space.
So lets go back to the bow and arrow.
What are the action-reaction pairs at work here?
There's the force of your fingers pulling back the string,
and the string and bow reacting
by pulling back against your fingers.
When your fingers release the string and the arrow,
the string exerts a force on the arrow,
pushing the arrow forward.
The reaction is the arrow pushing on the string.
And while we're looking at that speeding arrow,
remember from another lesson...
as soon as the arrow leaves the string,
there is no more horizontal acceleration
because there's no more horizontal force.
The bow has done its job.
However, gravity is a force
constantly pulling the arrow down vertically.
Gravity from the Earth pulls on the arrow,
the arrow pulls back on the earth.
And now you know, forces work in pairs.
And you've seen some of the ways forces work together
to make things move.
That's it for this segment of "Physics in Motion".
We'll see you next time.
For more practice problems,
lab activities, and note taking guides,
check out the Physics in Motion tool kit.