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Hi, myself Sufal Kumar,
Physics Faculty.
Dear friends, viewers & students, my channel is about Physics Education. I am to concentrate mainly on JEE, NEET, CBSE & ISC in near future.
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Hi, myself Sufal Kumar,
Physics Faculty.
Dear friends, viewers & students, my channel is about Physics Education. I am to concentrate mainly on JEE, NEET, CBSE & ISC in near future.
#sufalphysicsforum
#jee
#neet
#physics
#cbse
#iitjee
#igcse
#cbse12thexam
Pls like, share & subscribe, if you like my educational video....
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LearningTranscript
00:00Energy equals to mass into speed of light?
00:06Energy is mass into speed of light square.
00:09E is equal to mc square.
00:14From this equation, mass and energy can be converted into each other, provided mass is
00:23moved with speed of light or comparable speeds.
00:29Suppose you are thrown in space with speed of light, then you will start converting into
00:43energy.
00:44I will become an energy.
00:47Yeah, you will be getting transformed into energy.
00:51My body, my mass, my everything will be energy.
00:54I will no longer be a physical entity.
00:56Yes.
00:57What?
00:58In a way, energy is also a physical entity.
01:02But it is another form.
01:03Wow.
01:04This is really cool.
01:07So this is a significance of E is equal to mc square.
01:13How do they even find this?
01:14Is it theoretical or is it practical?
01:17No.
01:18It is practical.
01:19What?
01:20They've done this?
01:21They've tried it?
01:22It is a foundation for a theory of relativity.
01:23Who did it?
01:24What?
01:25Albert Einstein.
01:26No, but how did they find it?
01:27Yesterday, I had one video, I have saved in the form of screen recording, how speed
01:38of light in air was detected.
01:42That was the video.
01:47Okay.
01:50So hello friends.
01:51I'm going to derive E is equal to mc square.
01:56This is the most popular equation of the universe.
02:01This is basically Einstein's mass energy equivalence.
02:05That means according to this equation, energy and mass are interconvertible provided this
02:15mass m is moved through the space with the speed equivalent to speed of light.
02:24Initially it was a theoretical concept while Einstein proposed this equation, but later
02:31on, according to this theoretical assumption given by him, plenty of practical research
02:39underwent and because of these developments, today our space science is what we see today.
02:48So let's move on to proof.
02:51E is equal to energy, m is mass and c speed of light.
02:59What we know is 3 into 10 raised to 8 meter per second.
03:03That means 3,00,000 kilometers per second, but absolute value of speed of light is 2,99,793,458
03:15meter per second.
03:18Approx 3,00,000 kilometer per second.
03:23For proving we need to consider work energy theorem in general.
03:28What we people study in work energy power that work is done is equal to change in kinetic
03:36energy.
03:37The work done in the process will change kinetic energy mass m.
03:52Change in kinetic energy is equal to work done dE is equal to Fdx.
04:04Now from Newton's second law of motion, F is equal to dp by dt.
04:11That means rate of change of momentum with respect to time, rate of change of momentum.
04:17That means where p is momentum and also dx by dt is v.
04:26Now I am to include the value of dp by applying product rule.
04:37You know for this differentiation purpose we were bound to consider this kind of differentiation
04:43because mass is also here variable.
04:47Then coming back while putting this value of dp in the equation dE is equal to vdp.
04:56This can be is considered as equation number 1.
05:01Relation between absolute mass and relative mass from the theory of relativity only.
05:14The relation being m is equal to m0 root under 1 minus v square upon c square.
05:23Now I am going to explain the notations where v is the speed of that mass which is thrown
05:31into the space.
05:32m0 is absolute mass, m is relative mass.
05:37From here we can slightly manipulate m is equal to m0 1 minus v square by c square raise
05:49to minus 1 by 2.
05:52Now for the purpose of now we will be differentiating this equation to get dm by dv.
06:01Why?
06:02Because here we want to utilize this equation number 1.
06:06Now differentiating m0 being constant will be taken out.
06:12Now this time chain rule of differentiation nx n minus 1 then thereafter differentiation
06:21of this bracket nx n minus 1 then thereafter differentiation of this bracket that means
06:301 minus v square by c square.
06:321 is again 0 minus v square that means 2v 2 minus 1 that means 2v only.
06:43Similarly c square is constant so will be taken as it is further solving this minus
06:52cancels dm by m0 1 minus v square by c square minus 3 by 2 v square by v by c square.
07:05Now the appropriate rearrangement of terms are to be taken m0 1 minus v square by c square
07:13minus 1 actually I have factorized minus 1 v by c square that is equal to now I am to
07:26take reference from here the purpose for factorization was that only here we have m0 multiplied by
07:351 minus v square by c square raised to minus half and same term we are obtaining here also
07:44m0 1 minus v square by c square minus half so I am to replace this whole thing by m that
07:55was the motto c square minus v square by c square minus 1 v by c square now we want
08:06to reciprocate this will be cancelling then after that cross multiplication c square dm
08:15minus v square dm is equal to mv dv equation number 2 now after couple of steps we will have
08:25to perform integration so that we could do away with all these dm dm and dv let's see how do we
08:35arrange our equation it implies that already we had equation number 1 d e is equal to mv dv
08:48plus v square dm again take note of this d e is equal to mv dv plus v square dm equation number
08:561 we have obtained this in right hand side so c square dm could be written as d e now integrating
09:07both sides d e is c square dm it implies that delta e is it implies that this very equation
09:21delta e is equal to delta m c square is also used in nuclei where delta e is binding energy and
09:29delta m is mass effect but here for this simple understanding of e is equal to m c square we
09:38don't require so coming back to our final e is equal to m c square we have finally proved so I
09:49hope I could explain this equation very nicely and even then if you have any doubt you can always
09:57connect through comment box or other means of communication thanks a lot bye take care.