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Energy

# 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 :) 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
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.
• 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 ? • 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 :)
• • • 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) • 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) • 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..  