Particle 1 experiences a perfectly elastic collision with a stationary particle 2. Determine their mass ratio if the particles fly apart symmetrically relative to the initial motion direction of pa...
When they fly apart symmetrically relative to the initial motion direction with the angle of divergenceθ=60,
From the conservation of momentum, along the horizontal and vertical direction
and m1v1sin(θ/2)=m2v2sin(θ/2)
or, m1v1=m2v2 ...(2)
Now, from conservation of kinetic energy,
1/2 m1 v12+ 0 =1/2 m1 v12+1/2 m2 v22 ...(3)
From (1) and (2),
m1 u1=cos(θ/2)(m1v1+m1v1m2m2)=2m1v1cos(θ/2)
So, u1=2v1cos(θ/2)...(4)
From (2), (3) and (4)
4m1cos2(θ/2) v12=m1v12+m2m12v12/m22
or, 4cos2(θ/2)=1+m1/m2
or,...