Einstein mass energy relation Proof Derivation
Mass is defined as the property of the body as it resist its change
in position when some external force is applied on it. Mass is the quantitative
measure of inertia. Energy is defines as the capacity of the body to work it
may be of any kind .Energy exits in many shapes in the world. According to
Einstein Mass and Energy are interrelated and can be converted from one form to
another. Energy can be converted into mass and Mass can be converted into
Energy. According to newton’s second law of motion, the force acting
on body is equal to rate of change of momentum it produced. If a body of mass m moving with velocity v has a Force F applied to it, then.
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| Einstein mass energy relation Proof Derivation |
F=d/dt (mv)
F=m (dv/dt) +v (dm/dt)
If force F acts for small distance dx, the
work done Fdx stored in body as its kinetic energy is given by.
dK=Fdx
= (mdv/dt+vdm/dt)
=mdx/dt.dv + v.dx/dt dm
I.e. dK= mvdv+v2 dm
----------------- (1)
Now m=m0 /√1-v2 /c2
Squaring on both
sides m2=m20 /1-v2/c2
I-e m2= m20c2 /c2 –v2
Now m2 c2 – m2 v2 =
m20 c2
Differentiating on both side we
get
2mdmc2 -2mdmv2 -2vdvm2 =0
Now
dmc2 =mvdv+v2 dm
------------------ (2)
Comparing
1 and 2, we get
dK =dmc2
Integrating
∫0k dK= ∫m0m dmc2
After solving we get
k= (m- m0) c2
K+m0 c2 =mc2
If we donate total
energy by E, we get
This is known as Einstein mass energy relation Proof Derivation.
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