A) In a cyclotron (one type of particle accelerator), a deuteron (of mass 2.00 u
ID: 1348357 • Letter: A
Question
A) In a cyclotron (one type of particle accelerator), a deuteron (of mass 2.00 u) reaches a final speed of 10.9% of the speed of light while moving in a circular path of radius 0.447 m. What magnitude of magnetic force is required to maintain the deuteron in a circular path?
N
b) A space station, in the form of a wheel 114 m in diameter, rotates to provide an "artificial gravity" of 2.90 m/s2 for persons who walk around on the inner wall of the outer rim. Find the rate of the wheel's rotation in revolutions per minute that will produce this effect.
3.53 rev/min
Your response differs from the correct answer by more than 10%. Double check your calculations.
3.53 is what I got for the second one but somehow it said the I have to check my calculations which I did couple times!
Please show work for both of them, Thanks.
Explanation / Answer
a) speed of dutron, v = 10.9% of c
= 0.109*3*10^8 m/s
= 3.27*10^7 m/s
mass of deutron, m = 2u
= 2*1.66*10^-27
= 3.32*10^-27 kg
magnetic force required, F = m*v^2/r
= 3.22*10^-27*(3.27*10^7)^2/0.447
= 7.7*10^-12 N
b) Apply, a_rad = r*w^2
==> w = sqrt(a_rad/r)
= sqrt(2.9/114)
= 0.1595 rad/s
= 0.1595*60/(2*pi) rev/min
= 1.524 rev/min
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