To complete your master\'s degree in physics, your advisor has you design a smal

Question

To complete your master's degree in physics, your advisor has you design a small, linear accelerator capable of emitting protons, each with a kinetic energy of 10.7 keV. (The mass of a single proton is 1.67 10-27 kg.) In addition, 1.00 109 protons per second must reach the target at the end of the 1.80-m-long accelerator.

(a) What the average power must be delivered to the stream of protons?

(b) What force (assumed constant) must be applied to each proton?

(c) What speed does each proton attain just before it strikes the target, assuming the protons start from rest?

Explanation / Answer

a) P = N E/t = 1.0E9*10.7E3*1.6E-19= 1.7E-6 J

b) W = F d

F = 10.7E3*1.6E-19/1.8= 9.51E-16 N

c) KE = 1/2 mv^2

10.7E3*1.6E-19=0.5*1.67E-27*v^2

v= 1.43E6 m/s

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