Two protons approach each other with different speeds. (a)Will the magnitude of

Question

Two protons approach each other with different speeds. (a)Will the magnitude of the total momentum of the two proton systembe (1) greater than the magnitude of the momentum of either proton,(2) equal to the difference between the magnitudes of momenta ofthe two protons, or (3) equal to the sum of the magnitudes ofmomenta of the two protons ? Why ? b) If the speeds of the two protons are 340 m/s and 450 m/s,respectively, what is the total momentum of the two proton system ?[ hint: Find the mass of a proton in one of the tables ] Two protons approach each other with different speeds. (a)Will the magnitude of the total momentum of the two proton systembe (1) greater than the magnitude of the momentum of either proton,(2) equal to the difference between the magnitudes of momenta ofthe two protons, or (3) equal to the sum of the magnitudes ofmomenta of the two protons ? Why ? b) If the speeds of the two protons are 340 m/s and 450 m/s,respectively, what is the total momentum of the two proton system ?[ hint: Find the mass of a proton in one of the tables ]

Explanation / Answer

Let the mass of the proton = m Velocity of first proton = v1 Velocity of second proton = v2 Hence momentum of first proton is P1  =   m v1 Moment of second proton is P2   = m v2                 Magnitude of total momentum of twoprotons is :                   P   =   P1   +    P2                        =   m v1   +   m v2 As they are approcingeach other the directions of protons may be opposite to eachother .              P   = m v1   - mv2                       =   m (v1 - v2) Hence magnitude of the totalmomentum of the two proton system be equal to the differencebetween the magnitudes of momenta of the two protons. (b)          P = m (v1 - v2)              = 1.672 x 10-27   kg (340 - 450 m /s)              = 183.92 x 10-27      kg - m /s Hope this helps u!                          

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