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Lorentz Transformation

  • Thread starter Messy
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Homework Statement



An electron with rest mass m0 = 9.11E10-31 kg and charge e= 1.6E10-19 C was accelerated with an acceleration voltage U=30 kV

a) What is its velocity , momentum and energy in a classical picture ?
b)What is its velocity , momentum and energy in a relativistic picture ? What is its relativistic mass ?

c) If the acceleration voltage was only U=30 V , What is the electron's velocity , momentum and energy ? Would you use the classical or the relativistic picture and why ?

Homework Equations



For Part a) v = dx / dt
p = mv
energy = (1/2) m0 * v2

For Part b) Lorentz Transformation for Velocity
ux' = [ux - v] / [ 1+ (vux /c^2) ]
Where ux' as i understand is the velocity , moving frame of reference .

Relativisitc momentum
p= m0 * u / ((1-(u^2/c^2))^1/2

Relativistic Energy
E=mc^2

Relativisitic mass
mr = m0 / ((1-(u^2/c^2))^1/2



The Attempt at a Solution



If the above equations are correct in this case so

For part a) for velocity i m not getting how can i calculate the numerical figure
for momentum offcourse if i have velocity i can simply put it in the equation
for energy as well i need velcocity

For part b)

for velocity what is the difference in Ux and V ?
What U i have to substitute for relativistic momentum ?
For Energy :
mass = 9.11 E 10 -31
For Relativistic mass
m0 = 9.11 E 10 -31

Thanks in advance
 

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