Two projectiles (A & B) are fixed in opposite directions and simultaneously stri

Question

Two projectiles (A & B) are fixed in opposite directions and simultaneously strike and become embedded in a 1.0 kg mass. The mass is suspended vertically from a pivot point using a slender rod of negligible mass. The mass is free to swing in a circular arc of 10.0 radius Both "A & B " have a mass of 1.0 gram. Mass "A" has velocity of 626.73 m/s which if acting alone would cause the 1.001 kg combined mass to rise through 20.0m to top dead center. What must be the velocity at impact of mass B so that when A & B act together the combined mass of 1.002 kg rises to a height of 10.0 m and the rod is horizontal.

Explanation / Answer

now rod goes to only half the height.

that means energy of system after the collision is half that is in first case.

so momentum after the collision will be only 1/sqrt(2) times.

( 0.707 times)

angular momentum in first case = 0.001 x 626.73 x 10 = 6.2673 kg m^2 /s

So angular momentum in case2:

L = 0.707 x 6.2673 = 4.43165 kg m^2 /s

L = m vA R - m vB R

4.43165 = (0.001 x 10) (626.73 - vB)

vB = 183.5 m/s ........Ans

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