WEBVTT

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- [Instructor] Today in the gym,

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when my wife was doing dumbbell curls,

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I started wondering, see,
she's putting a force

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on that dumbbell upwards, right?

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But does that force stay a constant

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as she moves the dumbbell up or not?

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Does it change? And if it does
change, how does it change?

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Does it increase, does it
decrease? What happens to it?

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Guess what.

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We can answer this question by the end

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of this video using Newton's second law.

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So let's start with a simpler example.

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We have a ice hockey ground over here,

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and there's a puck moving
on top of it at some speed.

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If there are no frictional
forces acting on this,

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if you assume that, then the
forces acting on this puck

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would be balanced because in
the horizontal, you can see

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that there are no forces
because we're ignoring friction.

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And in the vertical,
the gravitational force,

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which is pulling down on
it is completely balanced

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by the force that the
ground is pushing up on it,

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the normal force, they balance it out.

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And so since there are no
unbalanced forces acting

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on this puck from Newton's first law,

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we know that this thing will
continue its state of rest,

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or in this particular case,
the state of uniform motion.

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So it'll continue to move
with that same velocity.

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But now comes the question,

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what if there was an
unbalanced force acting on it?

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What happens because of that?

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Well, let's find out.

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For that, let's just whack
it with a hockey stick.

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No.
(instructor laughing)

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So if I whack it to the
right, let's say in this case,

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I will now put an unbalanced
force to the right.

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What will happen? Well,
we can probably guess it.

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That puck's velocity will now be higher.

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It'll just get blasted off over there.

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So its velocity will increase.

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In other words, it will accelerate.

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Ooh, this means when there's
an unbalanced force acting

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on a an object, in other words,

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if there is a non-zero net
force acting on an object,

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which is the same thing as
saying an unbalanced force,

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but whenever this net
force acts on an object,

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what does it do?

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It accelerates our puck.

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The puck undergoes, or the
object undergoes an acceleration.

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This is the essence of
Newton's second law.

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Now all we gotta do is
analyze the situation

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even more carefully

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and see if we can concretize
this relationship.

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So let's do that.

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The first question we could have is yeah,

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so a net force causes an acceleration,

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but how long does that acceleration last?

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Well, let's see.

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When the stick hits the puck,

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that's when it starts accelerating,

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which means as long as
the stick is in contact

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with the puck, as long as
it's in contact with it,

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like right now here, it's during that time

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there will be acceleration.

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But what happens once it loses contact?

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Once it loses contact, again,
net force goes to zero.

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And now coming back to Newton's first law,

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it'll continue moving with
that same increased velocity.

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This means the acceleration only happened

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during this time when the hockey stick

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was in contact with it.

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In other words, the
acceleration lasts as long

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as the net force lasts.

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Okay, next, let's think
about what would happen

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if the net force was higher?

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For that let's imagine
we whacked it harder.

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What's gonna happen now?

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Or you can imagine it'll get
blasted off even more faster,

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even faster, right?

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Which means it'll have a higher velocity

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when it loses contact.

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Ooh, that means there'll
be bigger acceleration.

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So if the net force is larger,

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it means you'll have
a larger acceleration.

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If the net force is smaller,
you get a smaller acceleration.

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In other words, we see
a direct relationship

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between acceleration and the net force.

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All right, what else can we deduce?

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Hey, let's think about the direction.

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What is the direction of the acceleration?

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Well, in this case, the
net force is to the right,

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and our puck's velocity

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is also increasing towards the right.

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So in this case, the
acceleration is to the right.

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So in this case, if the
net force is to the right,

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the acceleration is to the right.

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What would happen if the
net force was to the left?

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So let's imagine we whack that puck now

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to the left, what would happen?

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Well, we can again imagine the puck

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would now get blasted off to the left.

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But let's look at it carefully.

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Since the puck is already moving
to the right, if we push it

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to the left, now we're gonna slow it down.

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The puck will come to a stop first.

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It'll happen very quickly
that we won't even see it.

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But it has to happen before
going to the left, right?

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Which means when you go from here to here,

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notice even though the puck
is moving to the right,

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it is slowing down, which
means the acceleration

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is to the left.

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So when the net force is to the left,

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we're seeing an
acceleration is to the left.

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After that, its velocity
might increase to the left,

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which means again, the
acceleration is to the left.

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Ooh.

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So if the net force is to the left,

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the acceleration is to the left.

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If the net force is to the right,

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the acceleration is to the right.

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So the acceleration will
be in the same direction

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as that of the net force.

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Okay, is there anything else
that affects our acceleration?

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Well, let's see.

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If you come back over here,

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what if you use the same bat,

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whacked it with the same force,

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but instead of a puck,

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let's say there was a bowling ball

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moving with the same velocity.

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What would happen now?

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(instructor laughing)

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I'm pretty sure you can
feel it in your bones now.

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It would be much harder
to stop that bowling ball

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and make it turn backwards, right?

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I mean, the same thing will happen.

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You will slow it down, but
it'll be much, much harder.

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It'll take a much longer
time to slow it down,

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even though you're putting
the same amount of force.

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So the net force has stayed the same.

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But what has happened to our acceleration?

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Since the velocity changed
over a much longer time,

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the acceleration became smaller.

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Hey, why did the
acceleration became smaller?

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What changed?

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From the puck to the bowling
ball, the mass changed,

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the mass increased.

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So this means mass also
affects the acceleration,

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but how does it affect it?

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Well, we saw that the
mass increased right now.

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What did that do to the acceleration?

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It decreased, and this
is kind of intuitive.

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The bigger the mass, the
harder it is to accelerate,

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meaning the smaller the acceleration,

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which means acceleration
has an inverse relationship

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with the mass.

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So now, everything that we just
analyzed about acceleration,

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its direction, its
dependency on the net force,

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how it depends on the mass,

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all of it can be put down in an equation.

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And that equation is pretty
much right in front of us.

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So the acceleration will
equal the net force divided

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by the mass.

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This is our Newton's second law.

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And look, the equation
is saying the same thing.

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Direct relationship between acceleration

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and the net force, inverse
relationship between acceleration

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and the mass and the arrowheads are saying

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that acceleration and the
net force will always be

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in the same direction.

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Isn't it amazing that we can pack all

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of that information in just
one beautiful equation?

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And of course, you may
have seen this written

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as f equals ma in some
sources, it's the same thing.

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I like to write it this way

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because acceleration
is caused by the force.

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So once we decide the
force is and the mass,

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then the acceleration gets fixed.

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But anyways, what will happen
if the net force is zero?

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What if we plug in over here zero?

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Well, then the acceleration
also goes to zero.

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What does this mean?

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Well, this means we have all
the balance forces acting

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on an object.

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And if the acceleration is zero, it means

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that the velocity stays a constant.

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In other words, this
is Newton's first law,

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which says an object
continues to stay at rest

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or in uniform motion.

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That is zero acceleration, right?

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When there are no unbalanced
forces acting on it.

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So notice, Newton's first
law is just a special case

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of Newton's second law,

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which means this equation is
encompassing both the second

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and the first law as well.

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And finally, speaking
about Newton's first law,

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what we also noticed over
here is bigger the mass,

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smaller the acceleration.

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In other words, if the mass
is bigger, it is harder

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to change its velocity.

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It's much harder to do
that, which means objects

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that have more mass have more inertia.

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That's something again we
learned in Newton's first law.

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Inertia is the property due

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to which objects continue to stay at rest

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or continue to stay in
uniform motion, isn't it?

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It can fight acceleration,

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and we can now see what
inertia depends on.

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Inertia is the mass.

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More the mass of an
object, more than inertia,

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harder it is to accelerate.

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Newton's second law could arguably be

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the most important equation
of all of classical physics.

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I say classical physics
because we now know

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that if objects are moving
very close to speed of light,

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then this breaks down, it doesn't work.

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Now we'll have to resort

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to Einstein's theory of relativity.

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On the other extreme,

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if we consider extremely tiny particles,

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like subatomic particles like electrons,

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protons, and neutrons,
well, even over there,

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turns out Newton's laws don't work.

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So even over there, it breaks down.

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But as long as you don't
go to such extremes,

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this equation will work for us.

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So now let's see if we can apply this

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to our original question.

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When she just started moving the dumbbell,

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dumbbell's velocity was increasing.

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After that, let's say
there was a small phase

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during which the velocity was constant,

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and finally, when the
dumbbell is about to stop,

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its velocity is decreasing.

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So now the question is how
do we figure out what happens

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to the force that she's
putting on the dumbbell?

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Well, let's apply Newton's second law.

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For that, let's first think
about the acceleration.

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Well, over here, we are dealing
with increasing velocity.

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Therefore, the acceleration is upwards

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in the same direction as it's moving.

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Then we have a constant velocity,

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which means the acceleration is zero.

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Finally, we have a decreasing velocity,

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since the dumbbell is still
going up, decreasing velocity,

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which means acceleration must be down

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in the opposite direction.

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Now, because we know the
direction of the acceleration,

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we can figure out the
direction of the net force.

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It has to be exactly
the same, upwards here,

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zero here, downwards here.

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We are applying Newton's second law,

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the direction part over here.

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Now, finally, this is the
direction of the net force.

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We want to know what happens to the force

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that we are putting on the dumbbell

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or she's putting on the dumbbell actually.

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How do we do that?

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Well, let's look at all the
forces acting on the dumbbell.

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Well, we know that there's
gravitational force acting

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on the dumbbell all the time.

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That force is a constant,

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and therefore, our force is
in the opposite direction

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of the gravitational force.

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Now, in this case, when she's
just lifting the dumbbell,

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if the net force needs to be upwards,

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that means her force must be larger

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than the gravitational force.

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Only then her force will win out,

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giving a net upward force, right?

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Okay, what about over here?

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We want the net force
to be zero over here.

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How can that happen?

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Ah, her force has to be exactly the same

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as gravitational force

00:10:48.330 --> 00:10:52.470
because only then the forces get balanced.

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Finally, what happens over here?

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Well, we want the net
force to be downwards,

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which means we want gravity to win.

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That means her force must be smaller

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than the gravitational force.

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Look, even though we did
simplify it a little bit,

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I mean, I'm not really sure

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that her dumbbell was moving
at a constant velocity,

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but once we simplified a little
bit, we were able to analyze

00:11:11.970 --> 00:11:13.470
what happened to the force

00:11:13.470 --> 00:11:14.730
that she was putting on the dumbbell.

00:11:14.730 --> 00:11:18.030
It went on decreasing as
the dumbbell moved upwards.

00:11:18.030 --> 00:11:19.140
Isn't that incredible

00:11:19.140 --> 00:11:21.300
how we used Newton's second law do that?

00:11:21.300 --> 00:11:22.293
Amazing, isn't it?