1deleted for 9-10 didnt see
Why is it that momentum is mv while kinetic energy is 1/2 m v2
and not some other way.. like momentum is 2mv, while KE is mv2
A very very basic and important question which i would like some class IX-X students to answer first....
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10 Answers
11Kinetic Energy is the work done by the retarding force in stopping a moving body
or
K= FS.....(i)
But we know F=ma.....(ii)
and if for the moving body initial velocity=v
and final velocity=0(since the body will ultimately come to rest)
Now acceleration in this case=-a(since retardation=a)
So from the relation v2-u2=2aS.......(iii)
v2=u2-2aS(as acceleration=- a )
so S=v2/2a
Now as K=FS
so from eqn ii and iii
K= ma.v2/2a
or K= 1/2 mv2
Linear momentum(P)= product of mass and linear velocity
or P=mv
So any expression such as P=2mv or K=mv2 flouts the basic defination of momentum and Kinetic Energy and hence not possible
23hey i think momentum is a quantity defined just to simplify mechanics.
momentum can also be 2mv , but it was defined mv so cant help .
Momentum be 2mv or mv , its properties wont change , i.e conservation of momentum when no external forces act , etc etc
is it correct ?
1CRUDELY SPEAKING .....momentum signifies "QUANTITY OF MOTION" possesed by a body...and it has two components...
(i)mass
(ii)velocity
(iii)since we want a "QUANTITATIVE" idea so we got to have a factor "1" too
now from fundamental PRODUCT RULE of COUNTING we get:
QUANTITY OF MOTION=1*m*V
1so for getting an idea of "QUANTITY" of motion that factor "1" is quite important......had we got to study some "PROPETIES" of motion.....any other factor like 2,3,4,.........would have equally worked well!
49i think qwerty is correct....
it is just a convetion
K.E= mv2/2 is just a result of the convention p=mv
but p=mv is just plain simple convention!!:)
1thth factor ONE is important......n tht favor is done to momentum for the sake it represents the QUANTITY OF MOTION POSSESSED BY THE BODY!
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