CHAPTER 6. MOTIONIN TWO DIMENSIONS 6.3
x-component of momentum:
pi 1 x = m 1 vi 1 x= m 1 vi 1 cos θ 1
pi 2 x = m 2 ui 2 x= m 2 vi 2 cos θ 2y-component of momentum:
pi 1 y = m 1 vi 1 y= m 1 vi 1 sin θ 1
pi 2 y = m 2 vi 2 y= m 2 vi 2 sin θ 2After the collision
Total momentum:
pf 1 = m 1 vf 1
pf 2 = m 2 vf 2x-component of momentum:
pf 1 x = m 1 vf 1 x= m 1 vf 1 cos φ 1
pf 2 x = m 2 vf 2 x= m 2 vf 2 cos φ 2y-component of momentum:
pf 1 y = m 1 vf 1 y= m 1 vf 1 sin φ 1
pf 2 y = m 2 vf 2 y= m 2 vf 2 sin φ 2Conservation of momentum
The initial momentum is equal to the final momentum:
pi= pfpi = pi 1 + pi 2
pf = pf 1 + pf 2This forms the basis of analysing momentum conservation problems in twodimensions.
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