A particle of mass MA traveling with speed UA1 experiences a perfectly elastic h

Question

A particle of mass MA traveling with speed UA1 experiences a perfectly elastic head-on collision with a stationary target particle of mass ms. (a) Demonstrate. CLEARLY, that the velocities of the two particles immediately after the collision are given by: Simplify the above in the instance that mA me: i.e. when the mass of the target particle is much smaller than the mass of the other particle. Simplify the above in the instance that mA = mB: i.e. when the mass of the target particle is equal to the mass of the other particle.

Explanation / Answer

a)   Here, applying conservation of momentum

=> mA * vA1 + 0   = mA * vA2 + mB * vB2

Also, due to elastic collision

=>   1/2 * mA * vA12 + 0   = 1/2 * mA * vA22 + 1/2 * mB * vB22

=> Solving for vA2    and    vB2

=>     vA2   =   (mA - mB)/(mA + mB) * vA1

=>      vB2   =   (2mA)/(mA + mB) * vA1

b)   If mA << mB

=>   vA2   =   - vA1

=>    vB2   =   0

c)   If   mA >> mB

=>   vA2   =   vA1

=>    vB2   =   2vA1

d)   If mA = mB

=>     vA2   =   0

=>      vB2   = vA1

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