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Welshy
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Homework Statement
A sphere of mass m1 traveling at velocity u1 collides elastically with a stationary sphere of m2. The particles move away with v1 and v2 respectively.
I'm at part 4, of 5. It asks us to resolve the conservation of momentum equations normal and tangential to the post-collision velocity of m2. I obtained these equations using the diagram that's provided. The part I'm stuck on is where they ask us to obtain an expression for tanB involving only the masses and angle A.
A = angle of incidence
B = angle of reflection
The 5th part asks "Hence when does the angle of incidence equal angle of reflection?". So I know the resultant equation should be something along the lines of:
tanB = ((m1 + m2)/m2)*tanA
as m1 should be << m2
Homework Equations
m1u1cosA = -m1v1cosB + m2v2
m1u1sinA = -m1v1sinB
m1u12 = m1v12 + m2v22
The Attempt at a Solution
I found terms for v1 and equated them eventually getting:
tanB = ((m1u1cosA)/(m1u1cosA - m2v2))*tanA
But now I'm stuck. Any pointers?
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