Download of Newton`s Second Law of Motion Video Script

Physics 403 – More of Newton’s Second Law
(Read objectives on screen.)
Instructor
Welcome back. Would you believe I bowled a perfect game?
What about this? Would you believe that this ball and this marble would fall at the same rate if I
dropped them together? And what would that rate be on earth?
If you said that they both would accelerate at 9.8 m/s2, you’re right. Let’s see why.
Many students, especially the surfer types, will say that gravity pulls the ball and the marble the same.
Do you really believe that? What do we call the force of gravity pulling on an object?
I hope you said weight.
So what if we weighed the bowling ball and the marble? Of course they don’t weigh the same. The
force of gravity pulling the ball toward the earth is much larger than the force pulling on the marble.
If only weight were involved, the acceleration of the ball would be much larger than the acceleration
of the marble.
But we know that there’s more to it than that. It’s true that force causes acceleration. But it’s also
true that mass, or inertia, resists acceleration. And what do we know about the masses of the ball and
marble? Tell your teacher.
(table on screen)
The mass of the bowling ball has to be much larger than the mass of the marble, doesn’t it? That
means the ball has much more inertia than the marble. Since inertia resists acceleration, the bowling
ball’s inertia would resist acceleration more than the marble, so its acceleration will be much smaller
than the marble’s.
Now let’s look at the effects of both weight and mass, at the same time. If only weight, or the force of
gravity were involved, Aristotle would be correct, and the bowling ball would accelerate more. But if
only mass were involved, the marble would accelerate more because of its smaller inertia to resist
acceleration. So who wins? Let me fade out of the picture while you tell your teacher.
Instructor
The answer is that neither the bowling ball nor the marble wins the acceleration race. And that’s true
of all objects. Heavy objects will have both large weight and large mass, which have opposite effects
on acceleration.
And light objects like our marble, have small weight and small mass. The effects of mass and weight
on acceleration cancel out again.
cartoon of (scales on screen)
VO
The concept of all objects accelerating the same in free-fall is so important that we need to go over it
one more time. This time, let’s use math.
We have a 1.0 kilogram cylinder and a 10 kilogram cylinder. We know that on earth the one kilogram
cylinder will have a weight of 9.8 newtons. And that weight is the force of gravity pulling the
cylinder toward the center of the earth. When we know mass and force, we can calculate acceleration
using “F=ma”. Acceleration equals force divided by mass or 9.8 newtons divided by 1.0 kilograms.
The acceleration of a falling one kilogram cylinder is 9.8 m/s2.
Now let’s calculate the acceleration of the ten kilogram cylinder. Its weight on earth is 98 newtons.
When we calculate acceleration, we get 9.8 m/s2.
The heavier cylinder had ten times the mass of the lighter one and ten times the weight. The ratio is
always 9.8 m/s2 on earth. And we call that ratio “g,” the acceleration due to gravity.
(astronaut on screen)
VO
On the moon, the masses of our cylinders would stay the same, but their weights would be one sixth
as much. The ratio would be the same for both cylinders, or for bowling balls and marbles or
hammers and feathers. But it wouldn’t be nine point eight meters per second squared, but one sixth of
that or 1.6 m/s2. It looks like this NASA film is in slow motion, but it’s the real thing.
Instructor
Galileo knew that all objects in an airless environment would fall at the same rate, but he didn’t know
why. It was up to Isaac Newton to explain why. And now you can, too.
That explanation is based on what most physicists would tell you is the most important equation in all
of mechanics, “F equals m a.” Now, I’d like you all to practice explaining why heavy and light
objects fall at the same rate when there is no air to interfere. And don’t even think about saying that
gravity pulls all objects the same. That’s just not true because all objects don’t weigh the same. I
weigh much more than the smallest girl in your class, but I also have much more mass than she does.
That’s the key to understanding this concept. Your teacher will give you some time to practice, either
verbally or in writing. When you come back, we’ll talk about jumping out of airplanes.
(Pause Tape Now graphic)
Instructor
Earlier, you learned why objects in free-fall have the same acceleration, which we call “g.” What is
the condition required for free fall? In other words, what must be absent for an object like a piece of
paper, to fall freely?
If you said air, you’re right. If the objects are compact, like this wadded up paper and this book, and
don’t have to fall great distances, we say that they are in free fall, even if it’s not perfect. The objects
hit the table at the same time.
But look what happens when we flatten out the paper and drop it and the book together. They
certainly don’t fall at the same rate this time, do they? What’s different? This time, air resistance is a
big factor.
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(green chalkboard on screen)
VO
Air, or wind resistance is a force that acts on objects moving through the air. On falling objects, air
resistance acts upward.
Air resistance depends on two factors. One is the speed of the object. The faster the object moves the
more air molecules hit it each second.
The second factor is the surface area of the object. The larger the surface area of a falling object, the
more air molecules push it upward.
(skydiver on screen)
Skydiver wear baggy clothes and spread their arms and legs so that as much surface as possible can be
hit by the air.
(parachute on screen)
And when they pull the rip-cord, they want their parachutes to open wide, for maximum surface area
and maximum air resistance.
(bike, horse, etc. on screen)
You can experience air resistance by riding a bike, a motorcycle, or even a horse. The faster you go,
the more wind you feel. Remember that motion is relative. Moving forward through the air is the
same as standing still and having the wind blow straight into your face and body. Either way, it feels
the same.
Instructor
Now that you know what air resistance is and the factors that affect it, let’s see how air resistance
affects the motion of a falling object, like our piece of paper.
(force diagram on screen)
In a vacuum, the only force acting on the paper is its weight, which pulls the paper down to the earth.
So the paper’s acceleration would be its weight divided by its mass, which we know is “g” or nine
point eight meters per second squared.
But in the atmosphere, air molecules push upward on the paper, which means that the force of air
resistance acts in an upward direction. The net force is now weight minus air resistance. This reduces
the net force pulling the paper down, so its acceleration is decreased. There is still a net force acting
on it, so its velocity is increasing, but the rate of increase is less than before.
Instructor
Even though acceleration has decreased, the paper is still gaining speed. Eventually, the force of air
resistance will equal the paper’s weight. The question is “what happens next?” Think about it and tell
your teacher.
Physics surfers might say that the paper will slow down or stop. But that wouldn’t make sense. Let’s
look at the situation more thoughtfully.
(force diagram on screen)
The paper’s speed has increased until the force of air resistance equals the force of gravity or weight
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of the paper. The net force on the paper is now zero.
Instructor
This means that Newton’s First Law is now in charge. When no net force acts on a moving object, it
will continue moving in a straight line at constant speed. The paper doesn’t stop moving, it only stops
what?
It stops accelerating. We say that the object has reached terminal velocity.
(green chalkboard on screen)
VO
When the force of air resistance equals the weight of an object, the net force acting on it is zero.
The object’s acceleration is zero.
It has reached terminal velocity and will continue at that velocity for the remainder of its fall.
Instructor
Raindrops reach terminal velocity early in their trip to the ground. The bottom of each drop flattens
out as it falls, giving it a large surface area. And the weight of the raindrop is small, so it doesn’t take
much air resistance to equal the weight. Imagine what would happen if raindrops didn’t reach
terminal velocity, but kept on accelerating all the way down. They would be going so fast by the time
they reached the ground that they would act like little bullets, going right through this umbrella and
my head. Thank goodness for air resistance.
Now, while I get out of this rain, watch another group of people who appreciate air or wind resistance.
(sky divers on screen)
VO
“At any moment, the velocity of an object falling to earth is equal to the time it has been falling
multiplied by its acceleration. After 5 seconds of free fall, the velocity of a sky diver should equal 49
m/s. After 7 seconds, the velocity should be approximately 68.6 m/s. But the sky diver will not
achieve this velocity because wind resistance prevents an object from accelerating without limit.
Wind resistance exerts an upward force on objects falling toward earth. Because of wind resistance,
falling objects reach a velocity called terminal velocity. Terminal velocity is the maximum velocity
that can be achieved by an object falling in the air. Terminal velocity is reached when the upward
force of wind resistance equals the downward force of gravity. At that point the two forces being
equal and opposite balance each other, causing the object to continue to fall at a constant speed.
The terminal velocity of sky divers is approximately 54 m/s. Once sky divers reach terminal velocity,
they stop accelerating. When a parachute opens, the force of wind resistance increases. and they
begin to decelerate. This deceleration due to the increased force of wind resistance is what allows
parachutists to land safely.
(physics challenge on screen)
VO
Here’s a physics challenge for you.
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If two men of different weights have the same size parachutes and jump from a plane together, who
will reach the ground first?
a) the heavier man
b) the lighter man
c) neither (They will reach ground at same time.)
Tell your teacher.
(Pause Tape Now graphic)
(diagrams of parachutes on screen)
VO
The best way to answer this question is to draw force diagrams.
Let’s draw weight vectors first, a short one for the lighter man and a long one for the heavier man.
Since the surface areas of the parachutes are equal, if the men are falling at the same speed at one
point, what will you know about the air resistance acting on the men?
Air resistance will be the same. Let’s say that the men are falling fast enough for air resistance to
equal the lighter man’s weight.
The net force on the lighter man is now zero. This means that the man has reached his terminal
velocity. But what about the heavier man? There is still a net downward force on him, so he will
continue to accelerate. His terminal velocity will be greater than the lighter man, so he will reach the
ground first. The answer is “a.”
Instructor
Since we live in an environment filled with air, we expect heavier objects to fall faster than lighter
ones. Now you know that it’s all about air resistance, weight, and net force. I think it’s time to do
some math on this topic. Watch, listen, and learn.
(text on screen)
VO
Here’s our problem. “A skydiver has a mass of 57 kilograms and weight of 560 N. At one point the
air resistance acting on her is 130 N. What is the net force acting on the skydiver? What is the
skydiver’s acceleration?”
The solution will be based on Newton’s Second Law, “net force = m a.”. But this time, there are two
forces acting on the girl. It’s easy to find the net force if you just draw a force diagram. The weight
acts downward and the force of air resistance acts upward. Net force is 560 newtons minus 130
newtons, or 430 newtons downward. That means the acceleration will also be downwards.
Remember that net force and acceleration are always in the same direction.
Now we know net force and we want to solve for acceleration. What else do we need before we can
use F = ma? We need mass, which is 57 kilograms. Now we can calculate acceleration, which is net
force divided by mass. The skydiver’s acceleration is 7.5 m/s2.
Instructor
To solve problems involving two forces acting on an object, always draw a force diagram.
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Net force will be the large force minus the small force.
And we already know that net force equals mass times acceleration.
So put the two together and you get this equation to use when two forces act on an object.
Don’t forget that the direction of the acceleration will be the same as the direction of the larger force.
Maybe we need to work one more problem together before you try some on your own.
(text on screen)
VO
Our next problem is this. “After the skydiver, weighing 560 N, opens her parachute, the force of air
resistance becomes 680 N What does her acceleration become?“
We already know, from the last problem, that the mass of our skydiver is 57 kg. Now let’s draw a
force diagram. The larger force is the air resistance of 680 newtons upward. This means that our net
force will be upward and the acceleration will also be upward. We could use signs for this or we
could just use words. When we use the equation, large force minus small force equals mass times
acceleration, all we have to do is plug and chug. Our answer is 2.1 m/s2 upward. Since the skydiver
was falling downward, this acceleration will be a deceleration or negative 2.1 m/s2.
(text on screen)
VO
Now it’s time for you to try a problem. Your teacher will give you time to solve this problem. When
you come back, we’ll go over it together. Don’t forget to draw a diagram. And remember that the
direction of the larger force will be the direction of the object’s acceleration. Air resistance is
negligible in this problem.
Local Teachers: Turn off tape and give students problem set number one from facilitator's guide.
(Pause Tape Now graphic)
(text on screen)
VO
The first part of this problem may have tricked you because it’s too simple. Once the crate starts
moving uniformly, the net force to keep it moving that way is zero. That’s Newton’s first law. This
doesn’t mean that the helicopter exerts no force. Let’s make a force diagram of the two forces acting
on the crate. The rope is pulling it up and its weight is pulling it down toward the earth. Since the net
force is zero, the forces must be equal.
Now let’s look at the second part. When the helicopter accelerates upward, so does the crate. So now
there is a net force exerted on the crate upward. The net force equals mass times acceleration or 250
kilograms times 6.6 m/s2. The weight of the crate has not changed, so the upward force exerted by the
helicopter by means of the rope must increase.
Instructor
Do you see why ropes sometimes break or people lose their grips when being rescued? When you are
lifted uniformly, the net force is zero, which means the upward force equals your weight.
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But when you are accelerated upward, the upward force can be much greater than your weight. That
can create all kinds of problems.
Now it’s time for you to practice this kind of problem and take a quiz. When we come back, we’ll
look at Newton’s third law of motion.
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