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A) How much work is required to accelerate a proton from rest up to a speed of 0.980 c?

B) What would be the momentum of this proton?
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A)

Given that

Speed of proton, v = 0.989c

work = increase in energy

So, W = m?c^2 - mc^2 =m(?-1)c^2

here, ? = 1/?[ 1-(v/c)2 ] = 1/?[ 1-(0.989c/c)2 ] = 6.76

work = 938*(6.76 - 1) = 5403.46 MeV = 5.403 GeV

B)

m = rest mass of proton = 1.67 x 10^-27 kg

The velocity of light, c = 3 * 10^8 m/s

Velocity of proton, v = 0.989c

We have a formula for the momentum of the proton as

p = mv / ?[ 1-(v/c)2 ]

= (1.67 x 10^-27)(0.989c) / ?[ 1-(0.989c/c)2 ]

= 3.35 * 10^-18 kg m/s
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