In Newtonian Mechanics, the Newtonian Kinetic Energy KEN of a particle with mass m and velocity v is defined as 1 KEN=mv². 2 In Einstein's Theory of Relativity, the Total Energy of such a particle is defined as mc² √1-(v/c)²¹ where c≈ 3.0 x 108 meters/sec, and the Relativistic Kinetic Energy KER is defined as E= KER E-mc² = mc² 1 √1-(v/c)²
In Newtonian Mechanics, the Newtonian Kinetic Energy KEN of a particle with mass m and velocity v is defined as 1 KEN=mv². 2 In Einstein's Theory of Relativity, the Total Energy of such a particle is defined as mc² √1-(v/c)²¹ where c≈ 3.0 x 108 meters/sec, and the Relativistic Kinetic Energy KER is defined as E= KER E-mc² = mc² 1 √1-(v/c)²
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Transcribed Image Text:In Newtonian Mechanics, the Newtonian Kinetic Energy KEN of a particle with mass m and velocity v is
defined as
1
KEN="
In Einstein's Theory of Relativity, the Total Energy of such a particle is defined as
mc²
√1- (v/c)²¹
where c≈ 3.0 x 108 meters/sec, and the Relativistic Kinetic Energy KER is defined as
-₁)
E =
mv².
KER = E-mc² = mc²
1
√1- (v/c)²
1
√1-x
Then, by substi-
a) Find the first four non-zero terms of the Maclaurin series for the function
tution, find the first four non-zero terms of the Maclaurin series for the relativistic kinetic energy KER
What do you notice?
b) Compare the Newtonian kinetic energy KEN and the relativistic kinetic energy KER of a particle with
mass m and velocity v by finding the ratio KER/KEN for v/c = 0.1, v/c = 0.5, and v/c= 0.8. What do
you notice?
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