- #1
Taylor T
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Homework Statement
Problem: An object of mass m1 elastically collides with an object of mass m2 =(3/2) m1 that is initially at rest. The less massive object has speed v1 and travels at an angle of θ1with its original direction (x-axis) after collision; the more massive object has a speed of v2 = (2/3) v1 and travels at an angle of θ2 after collision. What are the initial speed v0 of the less massive object and the two scattering angles, θ1 and θ2?
known values ( symbolically at least)
m1
m2 = 1.5 m1
v1f
v2f = 2/3 v1f
Finding:
v0
θ1
θ2
Homework Equations
Momentum Equations:[/B]
Pi=Pf
KEi=KEf
Before:
Px: m1*v0
Py: 0
E: 1/2 m1*v0^2
After:
Px: m1*v1f*cos(θ1)+3/2 m1 * 2/3 v1f cos(θ2)
Py: m1*v1f*sin(θ1)-3/2 m1 * 2/3 v1f sin(θ2)
KE: 1/2 m1* v1f^2+1/2 3/2 m1 (2/3v1f)^2
Combined:
(1)KE: v0^2=5/3 v1f^2
(2)Px: m1v0 = m1*v1f cos(θ1) + m1*v1f cos(θ2)
(3)Py: m1*v1f sin(θ1) = m1*v1f sin(θ2)
The Attempt at a Solution
Equation (3)simplifies to sin(θ1)=sin(θ2)
(4) θ1=θ2
plugging (3) into (2)
(5) v0 = 2*v1f cos(θ1)
plugging 5 into 1
(2 v1f cos(θ1) ) ^2 = 5/3 v1f^2
solving for θ1 you get θ1=arccos( sqrt(15) / 6 ) which means θ2=arccos( sqrt(15)/6) as wellFrom here I am stuck trying to solve for v0. I am also unsure if my value for θ is correct.Thanks for the help.
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