A small marble (MA = 12.0 g ) slides to the left with a velocity of magnitude 20

Question

A small marble (MA = 12.0 g ) slides to the left with a velocity of magnitude 20.0 cm/s on the frictionless, horizontal surface of an icy New York sidewalk and has a head-on, elastic collision with a larger marble (MB = 32.0 g ) sliding to the right with a velocity of magnitude 50.0 cm/s . Let +x be to the right. (Since the collision is head-on, all the motion is along a line.) (Figure 1)

B) What is the magnitude of the total momentum of the system before the collision in g-cm/s?

C)What is the magnitude of the smaller marble's velocity after the collision?

Explanation / Answer

A.

Magnitude of momentum before collision is (---> +x direction)

Pi = ma*Va1 + mb*Vb1

Pi = 12*(-20) + 32*50 = 1360 Kg.m/sec

B. Conservation of momentum gives

Pi = Pf

1360 = 12*Va2 + 32*Vb2

And elastic collision condition

Vb1 - Va1 = Va2 - Vb2

50 - (-20) = Va2 - Vb2 = 70

Va2 = 900/11 = 81.81 m/s

Vb2 = 130/11 = 11.81 m/s

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