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Maximum angle of deflection

  • #1

Homework Statement



Hey, I was studying this problem and solution (by Rudy Arthur):

http://www.feynmanlectures.info/solutions/maximum_angle_deflection_sol_1.pdf

What I wasn't sure was why this solution only works for m<M. At which point did we restrict ourselves to m<M. How about when m>M?

Homework Equations



sin(theta) = m/M

The Attempt at a Solution



Clearly if m>M, the equation for deflection is undefined.

Thank you!
 

Answers and Replies

  • #2
104
0
Your question has the answer in itself!!
The reason, the solution is correct only for m<M is because the value of sine of an angle cannot be greater than 1, as you have already said. Even if you do not take m<M, after you reach the equation 6, and you try to determine its extremal value, the expression 7 clearly indicated why you cant take m>M, if you do or your v1 will turn out to have an imaginary value, which is not possible!!

It itself tells you that in this case for a maximum deflection angle of deflection to exist the value of m has to be less than M.
 
  • #3
tiny-tim
Science Advisor
Homework Helper
25,832
250
Hi Markus! :smile:

(have a theta: θ :wink:)

I don't understand the logic behind finding an extremum for θ from dθ/dv1 = 0 …

θ and v1 reach an extremum at the same time (I think), so he might as well say dv1/dθ = 0. :confused:
 
  • #4
Thanks for the π²³ ∞ ° → ~ µ ρ σ τ ω ∑ … √ ∫ ≤ ≥ ± ∃ · θ φ ψ Ω α β γ δ ∂ ∆ ∇ ε λ Λ Γ ô, Tim!
 
  • #5
Thanks for your responses. I understand.
 

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