(a) What analysis model describes the horizontal motion of the protons above the

Question

(a) What analysis model describes the horizontal motion of the protons above the plane?

particle under constant velocity particle under constant acceleration     particle in uniform circular motion particle in simple harmonic motion

(b) What analysis model describes the vertical motion of the protons above the plane?

particle under constant velocity particle under constant acceleration     particle in uniform circular motion particle in simple harmonic motion

(c) Argue thatR =

would be applicable to the protons in this situation. (Do this on paper. Your instructor may ask you to turn in this work.)

(d) UseR =

to write an expression for R in terms of vi, E, the charge and mass of the proton, and the angle . (Use the following as necessary: vi, e, E, , and mp for the mass of proton.)
R =

(e) Find the two possible values of the angle . (Enter your answers from smallest to largest.)

(f) Find the time interval during which the proton is above the plane in the figure above for each of the two possible values of . (Enter your answers from smallest to largest.)

Explanation / Answer

a) for the motion in horizontal direction

particle under constant velocity

b)

for the motion in vertical direction

particle under constant acceleration

c) as the motion of projectile is also motion under constant accelertion in vertical direction and horizontal motion is constant velocity motion , which is same as proton's motion

we can apply same formula here by changing g to acceleration a

d)

for the expression of the range

in this case

acceleration ,a = e * E/mp

hence , R = vi^2 * sin(2*i)/(e * E/mp)

R = vi^2*mp* sin(2*i)/(e * E)

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