Power & Numericals - Work & Energy, Force & Laws of Motion, Science, Class 9 Video Lecture

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now that we have talked about work and
energy let us quickly talk about power
because these three are very closely
related to each other so what is power
power is the rate of doing work or rate
of transfer of energy so that means
power actually tells us how fast or how
slow work is being done let us suppose I
have to do work what is my work letters
of course I have to move a box from one
position to another position right so
for that what will I do I'll apply some
force so that the box undergoes
displacement and it reaches from point A
to point B now the question is different
people can do the same work in different
time interval somebody will do it very
slowly somebody will do it very fast so
that rate of doing work the rate at
which the work is being done that is
known as power let us take the example
of a person who is on a bycicle and
another person who's on a bike so what
happens if you tell them that both of
them have to reach a particular
destination what do you observe the
observe that the person on the bike
reaches there faster as compared to the
person on the buying cycle that's
because the power of the bite is more
that is the rate of doing work the rate
at which work is done is more in case of
bike as compared to them by cycle let us
take another example suppose you have a
small Inn and you ask her to run you
have another guy who is around saying 15
years old who's also little more
energetic so you will see that this guy
runs faster than the small girl now you
compute that guy with another applet who
is like full expert in running and
jogging so you will see that this guy
would be running the fastest so that
means the power of this guy is greater
than the power of this type and the
power of the sky is greater than the
power of the small little girl so power
is all about the rate at which
how fast on how slow you are doing a
particular watch so you see that this
stronger strongest value will take the
least time to reach a particular
destination the second guy will take
lesser time and the small girl will take
law of time to reach the same
destination so this is all about power
so how do we measure power the SI unit
of power is what 1 watt is defined as
the power when work is done at the rate
of 1 June per second so how do we
mathematically define power power is
given by work done by time taken or
energy transferred by time taken there
are some larger units of power like kilo
watt where 1 kilo watt is equal to
thousand watts so now that we have
talked about power let us talk about one
small thing which we missed out that is
commercial unit of energy so until now
we I stole that energy is measured in
joules but Joule is a smaller unit of
energy now you would have seen that when
either meter reading of your house comes
every month so a guy comes he checks
your meter and he tells you how many
units of electricity
have you used so what does that
electricity electricity is nothing but
electrical energy right but they do not
measure it in tunes they don't see that
you have utilized five thousand joules
of electrical energy they don't say it
like that so how do they tell it they
tell it in units they say that ok your
electricity usage is say 50 units so
what does that unit that is a commercial
unit of energy so the commercial unit of
energy is kilo watt hour so it is kilo
watt hour and how do we relate kilo watt
hour with joules
one kilo watt hour is equal to 3 point 6
into 10 to the power 6 students how do
we get that one kilowatt hour is 1 kilo
watt is thousand watts so this will be
thousand watts
multiplied by
our is 60 minutes and 1 minutes or 60
seconds so this is 16 to 60 seconds so
this becomes 3 point 6 into 10 to the
power 6 joules right so 1 kilo watt hour
is 3 point 6 into 10 to the power 6
joules and one unit which you generally
see me electricity bill that one unit is
nothing but one kilowatt hour so that
means if you see that your electricity
bill has 10 units of usage that means
how many joules of energy have used 10
into 3 point 6 into 10 to the power 6
toons
right okay so with this we will conclude
this lesson on work and energy and I
hope that I have been able to explain
you the basic concepts of work and
energy so let us try to solve some
problems based on whatever we have
studied so far so here comes problem 1
it says that a certain household has
consumed 250 units of energy during a
month how much energy is this in joules
so how many units one unit is equal to
one kilo watt hour right so 250 units
will be equal to 250 kilo watt hour
right now we know that 1 kilo watt hour
is equal to 3 point 6 into 10 to the
power 6 joules
therefore 250 kilo watt hour will be
equal to 250 in 3 point 6 into 10 to the
power 6 joules so this is equal to 9
into 10 to the power 8 joules so this
would be the energy in joules let us
look at the next problem it says an
object of mass 40 kg is raised to a
height of 5 meters above the ground
what is its potential energy so when you
raise an object to a height to some
height from the ground the object the
work done on the object when you raise
it to this height is loaded as potential
energy and we also know the expression
for potential energy as MGH so what is M
mass of the object which is 40 G is
acceleration
due to gravity that is 9.8 meters per
second squared and height is 5 meters so
this is 1 9 6 zero joules so this is the
potential energy of the object if the
object is allowed to fall find its
kinetic energy when it is halfway down
so now if you allow this object to fall
what happens this potential energy will
only get converted to kinetic energy so
now if you look at it at this point let
us call this point as a let us call the
lower point is B now at Point a the
total energy is potential energy at
point B the total energy is kinetic
energy so what happens at halfway so
halfway is Point C so at at Point C the
energy is 1/2 kinetic and half potential
so at Point C energy is partly kinetic
and partly potential right so that means
kinetic energy that is kinetic energy at
C will be equal to 196 zero divided by 2
because the total energy will remain one
nine six zero joules at every point as
per conservation of energy at every
point the total energy would be 196 zero
joules so at Point C Point C this total
energy is half kinetic and half
potential so kinetic energy would be 980
joules right ok so let us look at
problem three it says an electric heater
is rated 1500 watts how much energy does
it use in 10 hours so the power of the
heated is given as 1500 watts and the
time for which it is utilized is given
as 10 hours so what is 10 hours 10 hours
is 10 into 60 into 60 seconds so that is
one two three six zero zero zero seconds
now by definition of power we know that
power is equal to work done by time take
and energy transferred by time taken so
we can see that energy will be equal to
power multiplying by time that is equal
to 1500 multiplied by three six zero
zero zero seconds so that is equal to
five four zero into 10 to the power 5
joules which can be written as 54 mega
joules so this much would be the energy
that it will utilize in 10 hours let us
look at problem for an object of mass M
is moving with a constant velocity V how
much work should be done on the object
in order to bring the object to rest so
what is the initial velocity I mean we
normally denote initial velocity by U
and final velocity by V initial velocity
of the object here is given as V so let
me denote this V like this right so this
is my initial velocity what is my final
velocity now I want to do some work on
the objects such that the object comes
to rest so that means final velocity is
zero right so work done is even by force
into displacement what is force my
Newton's second law it is mass into
acceleration and what is displacement
from the third equation of motion v
square is equal to u square plus 2ei s
in this case v square is 0 u square is v
square plus 2ei s so from this we can
say s is equal to minus v square by 2 a
so here we you can write s as minus v
square by 2 a so this a and a will get
cancelled so this will be minus half MV
square so this much should be the work
done on the object this negative sign
shows that the force is opposite to
displacement that means the force should
be applied on the object in such a way
that it opposes the motion of the object
since this force opposes the motion that
is why the object finally comes to rest
let us look at problem five it says
calculate the work required to be done
to stop a car
of 1,500 kg moving at a velocity of 60
km/h so what is the mass of the car it
is 1500 kg s so it is moving with an
initial velocity of 60 km/h and what is
the final velocity finally I want to
stop the car so final velocity is zero
let me convert it into metre per second
so this becomes 16 mm divided by 60 into
60 so this becomes 16 point 6 7 meter
per second so we have to calculate the
work done so even in this case we can
say that work done is equal to force
multiplied by displacement forces mass
into acceleration and what is
displacement we will again apply third
equation of motion that is v square is
equal to u square plus 2 a s so s
becomes v square minus u square by 2 a
so in this case V is 0 so this is equal
to minus u square by 2 a so we will put
this value of s that is minus u square
by 2 ay a and a will get cancelled so
this becomes minus half mu square that
is minus half m is 1500 and what is U
square sixteen point seven into sixteen
point seven so this comes out to be
minus two zero eight four one six point
six seven five joules so needless to say
what does this negative sign show that
the work done is negative so it is
negative both means forces opposite to
the direction of displacement now let us
look at the last problem of the lesson
it asks find the energy in kilowatt hour
consumed in 10 hours by four devices of
power 500 watt each so what is the total
power involved so the total power
involved in this case will be 4
multiplied by 500 because 500 watt is
the power of each device and you have a
total of 4 devices so this becomes 2
thousand
what's that is equal to in kilo watts
because 1000 watts is equal to 1 kilo
watt so this is 2 kilo watt and for how
much time the energy is consumed the
time is given as 10 hours so therefore
we know that power is equal to energy
transferred per unit time so we can say
energy will be equal to power multiplied
by time so power is 2 kilo watts and
time is 10 hours so this becomes 20 kilo
watt hour so this is the energy consumed
in kilo watt hour intend 10 hours by the
4 devices right so I hope that with
looking at these problems it is little
clear to you that how do we approach
problems so this lesson was relatively a
simpler lesson so it is it was just that
you should understand the scientific
definition of hope you should understand
how much work and energy related what is
potential energy with the sky netic
energy and you should have some idea
about how to approach the problems so
practice more problems so that you can
make your concepts clearer so see you
are in the next lesson thank you please
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