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# Energy intro (kinetic & potential)

Let's explore what kinetic & potential energies are. Created by Mahesh Shenoy.

## Want to join the conversation?

- Hello. Kinetic energy formula is:

m*v^2

--------

2

Can anyone explain, what this 2 (below like divide from 2) means?

Why we should divide from 2? why is not enough just m (mass) multiple v^2 (v-speed)?

I learn through Lithuanian physics book. So letters is different but same meaning. Science is everywhere science. Thanks for answer :)(3 votes)- Read Carefully every thing.

Expression for kinetic energy:

Suppose a stationary object of mass 'm' moves because of an applied force. Let u be the initial velocity (here u=0). Let the applied force be F. This generates an accelaration a in the object, and , after time t, the velocity of the object becomes equal to v. The displacement during this time is 's'. The work done on the object, Work=Force(F)*Displacement(s)------(1)

Now, Force=mass(m)*accleration(a)....{according to newtons second law of motion}--(A)

Displacement (s)=u*t+1/2 a*t^2.....however initial velocity(u)=0.......(B)

therefore s=1/2 at^2.........B

Now putting (A) and (B) in (1)

W =ma * 1/2 at^2-----------(2)

(rearranging 2)

W=1/2 m(at)^2 ....exp-as 'a' was common in 'ma' and 'at^2' a*a=a^2 and t was already in square therefore (at)^2 .........

Hence W= 1/2 m(at)^2-------(3)

using Newtons first eqn of motion.....

v=u+at

as u=0

therefore V=at

by squaring on both sides

v^2=at^2......C .... we are squaring on both sides because in (3) there is (at)^2 to and here we just have v=at so we square it to make it equal to that to put in eqn and therefore there is v^2.

Now putting C in in place of at^2 ; v^2

therefore W=1/2 mv^2

(Imp)Now answer to your ques.

ans. we divide it by 2 because in Newtons second eqn of motion there is 1/2 at^2 it means divide by 2. and we had derived kinetic energy formula by Newtons second eqn of motion , first eqn of motion, and Newtons law of motion.

If you still dont understand then reply.I will have some other ways to make you understand.(8 votes)

- Visualize a rock. If I dropped the rock from a lower height then the energy would be less. If I dropped the rock from a greater height, then the energy would be more. However, doesn't the force of gravity decrease as the distance increases ?

If the force of gravity does decrease, then the force applied to the object would decrease. If the force decreases, then wouldn't the energy decrease as the work done would be less ?(3 votes)- The force of gravity does decrease when you increase distance...but the decrease is very very very small, hence negligible.

The energy increases when we increase height as more work has to be done to take that rock to a greater height against gravity

Mathematically speaking, PE = mgh

So if height(h) increases, and the decrease in acceleration due to gravity(g) is negligible...Potential energy(PE) will increase*Hope that helped...feel free to comment if your doubt persists :)*(3 votes)

- So, With a lot of light energy we can move a body?

Then Why isnt Mercury moving out of its orbit, being so close to the sun..?

I know this isnt related much to the topic but just asking..(0 votes)- Because Of Suns Gravity It Stays on Its own orbit And Also Sun Possesses 300000x more gravitational energy than earth(2 votes)

- So almost everything has energy.(1 vote)
- yes i have the same answer too the formula is m*v^2(1 vote)
- About your theory about using a laser to propel a space craft into space, the farther you go into space the more energy you need so will that really work?(1 vote)
- I don't really get your point. Why will we need more energy as we travel farther in space and what he told is completely right , we can do that , but it'd be more efficient if we do that with solar rays (from the sun)(1 vote)

- if book at some height is at rest and in that state the book cannot displace any other object by applying force

i.e the book do not have capacity to do work (energy)

then why we say that energy is stored in the book (it has potential energy )??

and how capacity to do work can stored in something ??(1 vote) - Please I don't really understand well,the problem I have is how to work it out, when I say any questions about, kinetic,potential,and work done,am always convinced, I need some help please.(0 votes)
- I don't understand what you mean.

Can you please elaborate?(2 votes)

## Video transcript

energy is a word that we keep using very frequently in our daily life but what is the scientific meaning of this term that's what we're gonna find out in this video so according to physics energy is the capacity to do work and before we try and figure out what this statement means let's quickly recall what work is in physics work is the force acting on an object multiplied by the displacement of that object this means to do work you need to push on something and make it move so what is the statement saying this statement is basically saying that anything that can do work has something called energy okay so if you can do work you have energy that's the basic idea behind it so anything that can push an object and make it move must have energy all right let's look at some examples this lady can push on this cart and make it move so she can do work on that cart therefore she must have energy so all living things can do work so all living things must have energy but can not living things air energy let's find out if I take a cricket ball and throw it at the stumps then it can do work on the stumps right I mean the ball pushed on the stumps and it made it move so the ball had energy let's take another example if I would drop a hammer onto a pin then it can do work on that pin it pushed on that pin and made it move so the hammer also had energy so what's common in both of these well over here before the ball hit the stumps it was moving so you see moving ball has the capacity to do work and therefore it has energy similarly over here before hitting this nail the hammer was moving so moving hammer has the capacity to work it must have energy as well and so can you see that any moving object must have energy the faster it moves the more energy it should have right because it can do more work and so we can give a name to this energy we can call this moving energy but in physics we do a more technical term it's called the kinetic energy and so energy of an object due to its motion is called kinetic energy and some other examples would include ring wind is moving air so that's kinetic energy even waves in water have kinetic energy because they're also we have motion okay but guess what we can also have energy without motion let's take some examples of that suppose we take a spring and compress it now if I keep a paper ball in front of it and let go of my hand you can imagine it can do work on the paper ball right because you can push on that ball and it can make that ball move that means this compressed spring has capacity to work it has energy notice that spring is not moving yet it has energy similarly if you take a stretched rubber band that should also have energy because even that can now shoot a paper ball and do work on it okay now the question over here is what does this energy depend on for example how can I increase the energy inside this spring well you might know if I can compress it more then it'll have more energy right because it can now shoot this ball with much higher force doing more work on it so compressing the spring has increased the energy similarly if I stretch the rubber band more over here it'll have more energy so over here what is the energy depend on the energy depends on how much you compress or how much you are stretching this object so in general we can say over here the energy depends on the configuration of the object basically it means how you are arranging that object how much you are stretching or compressing it now before we give a name to this energy let's look at one more example if I take a ball and raise it to some height and let's say I drop it then gravity can do work on that ball right because gravity can pull on it and make it move oh that means gravity itself must have energy in it it's a little hard to think about it right because we can't see gravity yet it must have energy because it can do work now again the question over here is what does the energy of gravity depend on you think about that how can I increase the energy of the gravity over here well I can just raise that ball higher right because if I raise it higher and now now I drop it from here the force of gravity would be the same but now it can displace more that means gravity would do more work whoo that means the energy of gravity has increased so the energy of gravity depends on the height higher I go more gravitational energy so in general we can say it depends on what it depends on the height or we can say it depends on the position of this object right so over here the energy depends on position but again to talk about the name of this energy what should we call it can you think of something that's common in all three of this what do you think is common over here think about it all right in all these cases if I let go of my hand the objects will gain kinetic energy I think about if I let go off my hand over here the ball will get shot like this here also the ball this ball will get shot like this here also if I drop the ball the ball will go down increasing its kinetic energy so it's as if in all the three cases they are waiting to become kinetic right these energies are waiting to become kinetic and that's why we call these energies potential energy so the word potential is basically saying these energies are waiting to be kinetic it's not a kinetic yet but it's potential it's just waiting for it okay and what is potential energy depend on well it can depend on the position of the object or it can depend upon the configuration of our objects all right so over here we can say the energy in gravity is gravitational potential energy similarly over here we can say the energy is elastic potential energy because the energy is coming due to elastic forces right due to the elastic nature of the material but they're all potential energies waiting to become kinetic and there could be other kinds of energies as well for example we might know light itself is a form of energy but this does light do work can light push on things and make it move well in our day-to-day life we may not see that happening but if you had a very powerful source of light then it could happen in fact you know what in future we think that's one way of space travel for example the idea is we can have a spacecraft and just shoot a very very powerful laser from the earth and that if it has enough energy that that laser can start pushing it and you know make that spacecraft move accelerating it so yeah light does have energy it can do work it can push on things and make them move and of course we could be other kinds of energies as well like heat energy sound energy electrical energy chemical energy and so on and you might learn about them in the future but once you do you will see that they're actually combination of kinetic and potential energies itself and that's why kinetic and potential energies are super super important and lately you might have heard of this another thing called dark energy this is something which nobody knows about we don't even know what this is exists or not nobody has seen it people believe that this should happen because people think that that's what's causing the universe to expand definitely fun stuff to read about but this is something that we have no idea about as of today all right so let's quickly summarize what we learned in this video anything that can do work must have energy and we mean these are two kinds of energies kinetic energy and potential energy kinetic energy the word kinetic stands for motion so it's the energy due to moving things anything that is moving can do work and so it must have energy faster it moves more kinetic energy it has but tension energy is the energy that's waiting to become kinetic that's one way to think about it and what does it depend on potential energy depends on the position or the configuration so for example if you look at the gravitational potential energy that depends on the height of this object for small Heights it can do less work so less potential energy at higher Heights more potential energy because gravity can do more work so position but we can also have configuration one example of that could be Springs or rubber bands so if you take a spring and you compress it a little bit less potential energy but if you compress it more then you have more potential energy