- #1

GayYoda

- 10

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## Homework Statement

Fast moving α particles of mass m make collisions in a cloud chamber with gas atoms of mass M and negligible initial velocity. After a collision, the velocities of the scattered α particles and the recoiling gas atoms are v and V respectively, the former being inclined at an angle θ and the latter at an angle φ to the original α particle direction

show that 2vcos(θ+φ)=(1-M/m)V

## Homework Equations

p=mv

cos(θ+φ)=cos(θ)cos(φ)-sin(θ)sin(φ)

## The Attempt at a Solution

Resolving horizontally i got [1] ∑p = mvcos(θ)+MVcos(φ) and vertically i got [2] mvsin(θ)-MVsin(φ). i squared both equations and added them together to get m^2v^2+M^2V^2+2mvMVcos(θ+φ)=(Σp)^2. I'm not sure how to work out the initial velocity