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 9.6 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 1.20-m-long accelerator.
(a) What the average power must be delivered to the stream of protons?
1 µW

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

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

Explanation / Answer

Aveerage power   = (n/t)E     =   10^9 *9.6KeV     =  9.6*10^12 eV

1eV   = 1.6*10^-19 J

p_avg   =   15.36 *10^-7 j /s = 1.536   *10^-6 w = 1.536 micro watt

---------------------------------------------------------

velocity v =   sqrt(2E   / m)

m= 1.67*10^-27 kg

E = 9.6*1.6*10^-19 j     = 15.36*10^-19 j

initial velocity    =   4.2*10^4 m/s

P_avg   = Force * velocity

Force = p_avg    / velocity      =    1.536*10^-6     / 4.2*10^4    =   0.36*10^-10 N

force on each proton      = 0.36*10^-10 / 10^9    = 0.036   N

-----------------------------------------------------

according to work energy theorem

(1/2)mv^2    =   force * displacement   

here d = 1.2 m

force   = 0.036 N

v   =    (sqrt2 * force*displacement / m )

plug the values and get the anwer

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