A stationary object with mass m B is struck head-onby an object with mass m A th

Question

A stationary object with mass mB is struck head-onby an object with mass mA that is moving initially atspeed v0. A) If the collision is elastic, whatpercentage of the original energy does each object have after thecollision? 50%? B) What does your answer in part a) give for thespecial cases i) mA= mB and ii)mA= 5mB? C) For what values, if any, of themass ratio mA/mB is the original kineticenergy shared equally by the two objects after the collision? Thanks very much! A stationary object with mass mB is struck head-onby an object with mass mA that is moving initially atspeed v0. A) If the collision is elastic, whatpercentage of the original energy does each object have after thecollision? 50%? B) What does your answer in part a) give for thespecial cases i) mA= mB and ii)mA= 5mB? C) For what values, if any, of themass ratio mA/mB is the original kineticenergy shared equally by the two objects after the collision? Thanks very much!

Explanation / Answer

the velocities of A and B after elastic collision are vA = (mA -mB)*v0/(mA + mB),kinetic energy KA =mAvA2/2 =mA(mA -mB)2*v02/[2(mA+ mB)2] vB = 2mAv0/(mA +mB), kinetic energy KB =mBvB2/2 =4mBmA2v02/[2(mA+ mB)2] initial energy K = mAv02/2 a) the percentage pA = KA/K = (mA- mB)2/(mA +mB)2 pB = KB/K =4mAmB/(mA +mB)2 b) i) mA = mB pA = 0, pB = 1 ii) mA = 5mB pA = 4/9, pB = 5/9 c) if pA = pB = 1/2 4mAmB/(mA +mB)2 = 1/2 8mAmB = (mA +mB)2 8mA/mB = (mA/mB +1)2 mA/mB = 3 ± 22

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