Einstein\'s famous equation relating mass and energy is usually written as E = m

Question

Einstein's famous equation relating mass and energy is usually written as E = mc2 This is the "rest" energy and ignores kinetic and potential energy of the mass. What is the "rest" energy of a 1 kg mass in joules? (Note: this is not a calculator problem, you need to pay attention to units; and not much else, just remember when you multiply powers, you add the exponents) Use 3.0E+08 meters per second for c (speed of light) Including the kinetic energy necessitates the slightly more complicated equation E2 =p2 c2 +m2 c4 where p is the momentum mv, and v is the velocity of the mass m Show how equation B simplifies to equation A if v=0. Show that the units are consistent in both terms on the right hand side of the equation e.g. both are J 2. What is the kinetic energy of a 1 kg mass moving at a velocity of 17,000 meters per second? (KE=1/2mv2) What is the total energy (use equation B)? How does this compare to answer A?

Explanation / Answer

A)

E=mc2

E=1 x (3x108)2

E=9 x 1016 J

B)

E2=p2c2+m2c2                            B

as

p=mv

putting this in equation B

E2=(mv)2c2+m2c4   

E2=m2v2c2+m2c4

so if v=0 the first factor will zero and

E2=0+m2c4

E2=m2c4

E=mc2

hence it prove

C)

K.E=1/2mv2

     =1.445 x108 J

D)

E=9 x 10^17 J

E)

it is 10 time than A

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