What is the limit for using the equation for deflection when m>M?

[MarkusNaslund19]

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!

 

[Mandeep Deka]

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 can't 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.

 

[tiny-tim]

Hi Markus!

(have a theta: θ )

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.

 

[MarkusNaslund19]

Thanks for the π²³ ∞ ° → ~ µ ρ σ τ ω ∑ … √ ∫ ≤ ≥ ± ∃ · θ φ ψ Ω α β γ δ ∂ ∆ ∇ ε λ Λ Γ ô, Tim!

 

[MarkusNaslund19]

Thanks for your responses. I understand.