A proton has 1836 times the rest mass of an electron. At what speed will an electron have the same momentum as a proton moving at 0.0088c? v=______c
I first started using m1v1=m2v2 but that is wrong
tried 1/sqrt(1836)*.0088c but was also wrong. I am just so lost and frustrated on this question. I ask of you for your assistance. If you could please explain your process so I can better understand the material I would be very grateful. Thank You for your time.
I first started using m1v1=m2v2 but that is wrong
tried 1/sqrt(1836)*.0088c but was also wrong. I am just so lost and frustrated on this question. I ask of you for your assistance. If you could please explain your process so I can better understand the material I would be very grateful. Thank You for your time.
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p = γmv
p is momentum, γ is the Lorentz factor, m is the rest mass, v is the velocity
For the proton:
γ = 1 / (1 - (v / c)^2)^(1/2)) = 1.0000387
Set the momentum of the proton and electron equal to each other:
p = (1.0000387)(1836m)(0.0088c) = γmv ---> m's cancel
(1.0000387)(1836)(0.0088c) = γv
γv = 16.1574c
Plug in what we know γ is equal to:
(1 / (1 - (v / c)^2)^(1/2)))v = 16.1574c
Solve for v: (I used my TI-89 calculator)
v = 0.99809c
I'm not sure if this is right, but that's the answer I got using the method I came up with.
p is momentum, γ is the Lorentz factor, m is the rest mass, v is the velocity
For the proton:
γ = 1 / (1 - (v / c)^2)^(1/2)) = 1.0000387
Set the momentum of the proton and electron equal to each other:
p = (1.0000387)(1836m)(0.0088c) = γmv ---> m's cancel
(1.0000387)(1836)(0.0088c) = γv
γv = 16.1574c
Plug in what we know γ is equal to:
(1 / (1 - (v / c)^2)^(1/2)))v = 16.1574c
Solve for v: (I used my TI-89 calculator)
v = 0.99809c
I'm not sure if this is right, but that's the answer I got using the method I came up with.