Block A, with a mass of 4.0 kg, is moving with a speed of 2.0 m/s while block B, with a mass of 8.0 kg, is moving in the opposite direction with a speed of 3.0 m/s.The center of mass of the two-block system is moving with the velocity of:
A)1.3 m/s in the same direction as A
B)1.3 m/s in the same direction as B
C)2.7 m/s in the same direction as A
D)1.0 m/s in the same direction as B
E)5.0 m/s in the same direction as A

Question

Quizplus · Accepted Answer

The velocity of the center of mass (V_cm) is calculated using the formula: V_cm = (m1v1 + m2v2) / (m1 + m2), where m1 and m2 are the masses, and v1 and v2 are the velocities of the two blocks. For block B, since it's moving in the opposite direction, its velocity is considered negative. Thus, V_cm = (4.0 kg * 2.0 m/s + 8.0 kg * (-3.0 m/s)) / (4.0 kg + 8.0 kg) = (8.0 - 24.0) / 12.0 = -16.0 / 12.0 = -1.3 m/s. The negative sign indicates the direction is opposite to the positive direction assumed for A, meaning it's in the same direction as B.

Block A, with a Mass of 4