Newton's 2nd Law of Motion - Force & Laws of Motion Video Lecture - Class 9

oh hello welcome to my laboratory my
name is Professor mark and today I'm
going to be talking about Newton's
second law of motion this is one of
three laws where Sir Isaac Newton
published in 1687 the laws explain the
interaction of forces and objects and
the way in which the motion of an object
is affected by force the second law is
an incredibly important law even a law
its form is rather simple
you may have seen it before and it's
normally expressed as a equals MA
today I'll explain this law and together
we'll explore the way in which we can
use it to predict how an object will
change its motion when an unbalanced
force acts upon it so what does the F
the M and the e stand for well F
represents the force on the object M
represents the mass of the object and E
represents the acceleration of the
object resulting from the applied force
so using this equation it is possible
for us to calculate the force acting on
an object of known mass by observing the
object's acceleration alternatively by
rearranging the equation we're able to
protect the acceleration of an object of
known mass as a result of the force
acting on it so you can see that this
equation is very useful now you should
note that F equals MA is in fact derived
from the more exact definition of the
second law which is that the force
equals the rate of change of momentum of
the object where momentum is
the feigned as the objects mass times
its velocity however today we'll study
the law in the form F equals MA and the
best way for us to do that is to do an
experiment
okay well here is our experimental setup
we have a block of wood here
representing our object and as you can
see it is resting on a very smooth
surface which is sooo smooth we can
assume that it provides no resistance to
the block moving on it we also have a
loading device here which we'll use to
apply a constant force to the block as
it moves along the surface we'll be able
to measure the force being applied to
the block by observing this Newton
spring balance this uses a spring which
has been calibrated to read force in
Newtons
as a loading arm moves it exerts a force
on my hand through the extension of the
spring and we get a reading of the force
being applied as shown by the scale here
so let's do an experiment to better
understand Newton's second law of motion
remember that it states that force
equals mass times acceleration now a
very important point to note is that the
force refers to the sum of the forces on
the object in a given direction for
example let's look at the forces in the
vertical direction on this block we have
the gravity force and the force from the
table onto the block these are
unbalanced and therefore the net force
on the Block in the vertical Direction
is zero so what does F equals MA tell us
about the vertical acceleration of the
block when the sum of the forces in the
vertical Direction is zero well let's
write down the equation and see we start
with the sum of the forces in the
vertical Direction equals the mass of
the block times the vertical
acceleration that is F equals M e with
the subscript V used to indicate that we
are considering the forces and
acceleration in the vertical direction
we then rearrange the equation to get
the sum of the forces in the vertical
direction
divided by the mass of the block equals
the vertical acceleration so taking the
sum of the vertical forces equal to zero
and it ends with n being used to
represent utens taking the mass of the
block as five kilograms and then using
the equation for acceleration we see
that this gives zero Newton's divided by
the mass of five kilograms which equals
the vertical acceleration and since zero
divided by five equals zero
it follows that the vertical
acceleration is zero with the unit's
meters per second squared we can see
that this is indeed the case by
observing that the block is not moving
so what if we introduce an unbalanced
horizontal force well the second law
tells us that if we have an unbalanced
force we will observe the object
accelerating so let's do that and see
what happens
well we're ready to perform the
experiment as a block moves along the
surface we will take a snapshot of the
position of the block at one-second
intervals this will help us identify the
change in motion of the block
the block has a mass of five kilograms
and we will apply a force of two and a
half Newtons
so let's see what happens
where we have the snapshot of the
positions of the block at one-second
intervals you can see that the distance
between the snapshots increases this
means that the velocity of the block is
increasing which means that the block is
accelerating under the action of the
force we can check the force which was
applied by looking at the recording of
the Newton balance during the test it
was attached to the block through a
magnetic link between the end of the
Newton balance and a magnetic insert in
the block when city starts you can see
that a force of two and a half Newtons
was applied remember that the surface
here provides no resistance to the
motion so the measured force is the only
horizontal force applied to the block
and is therefore the unbalanced
horizontal force so what will happen if
we apply a force twice as large let's
apply a force of five Newtons to the
block and see what happens
well looking at the snapshots at
one-second intervals you can see how the
block has moved a further distance for
each second under the action of the
larger vibe Newton's force this is a
result of the larger force increasing
the acceleration of the block if we have
a look at the recording of the Newton
bounce during the test we see that a
force of by Newton's was indeed applied
to the block
so now that we understand the way in
which the second law works let's use it
to predict the force required to
accelerate a block 10 times the mass of
the smaller blocks our challenge is to
predict the force we need to apply to
this large block of 50 kilograms to
achieve the same acceleration
experienced by the small five kilograms
block when it had a force of 5 Newtons
applied so let's use Newton's second law
to calculate the force required we first
have to calculate the acceleration of
the small five kilogram block with an
unbalanced force of five Newtons applied
the subscript s indicates that we are
referring to the small block for this
part of the calculation we calculate the
acceleration by writing the second law
in the form force divided by mass equals
acceleration so taking the unbalanced
force equal to 5 Newtons and the mass
equal to 5 kilograms this gives five
divided by five which equals one meter
per second squared to calculate the
force required to accelerate the large
block at 1 meter per second squared
we use the second law in the form force
equals mass times acceleration where the
subscript L indicates that we are
referring to the large block for this
part of the calculation so taking the
mass of the large block as 50 kilograms
and the acceleration the same as the
acceleration of the small block which we
calculated as 1 meter per second squared
this gives the force we need to apply to
the last block equal to 50 kilograms
times one meter per second squared which
gives 50 Newtons now this is interesting
since you can see Newton's second law
has told us that for a block with a mass
ten times larger we need to apply a
force ten times larger to get the same
acceleration in other words to achieve a
given level of acceleration more forces
required to accelerate an object which
has more mass so let's apply a force of
50 Newtons to the large block and see
what happens I've lined up the center of
the large block with the center of the
small block at time zero so that we may
observe the relative motion of the
blocks by observing the positions of
their center points so let's run the
experiment
you
while computing the positions of the
snapshots for the large blog with a
force of 50 Newtons applied and the
small block with a force of 5 Newtons
applied we can see that the distance
between the snapshots at one second
intervals are the same this is because
they are accelerating at the same rate
just as we predicted and if we have a
look at the recording of the Newton
balance during the test we see that a
force of 50 Newtons was indeed applied
to the 50 kilogram block so there we are
that's how you use Newton's second law
to control the motion of an object
so let's review what we've learned about
Newton's second law of motion
the law has expressed as force equals
mass times acceleration we noted that
the force is a sum of the forces on an
object in a given direction if this
equals zero then the acceleration of the
object is zero we also observed that if
we have a nonzero unbalanced force
applied to the object it will accelerate
the larger the force the greater the
acceleration and for objects with larger
mass we need to apply a larger force to
get the same acceleration as a smaller
block with a smaller force applied well
thank you very much for joining me today
and I look forward to you visiting again
for further information why don't you
visit my website learn with mac.com
where you'll find the tutorial on the
second law and the latest news what else
I'm doing so from me professor mark
until next time all the best bye