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 momentum of the center of mass of the two-block system is:
A)16 m/s in the same direction as A
B)16 m/s in the same direction as B
C)32 m/s in the same direction as A
D)12 m/s in the same direction as B
E)60 m/s in the same direction as A

Question

Quizplus · Accepted Answer

The momentum of the center of mass of the system can be calculated by adding the momentum of each block. The momentum of block A is $p_A = m_A \cdot v_A = 4.0 \, \text{kg} \cdot 2.0 \, \text{m/s} = 8.0 \, \text{kg} \cdot \text{m/s}$. The momentum of block B, moving in the opposite direction, is $p_B = m_B \cdot v_B = 8.0 \, \text{kg} \cdot (-3.0) \, \text{m/s} = -24.0 \, \text{kg} \cdot \text{m/s}$. Adding these momenta gives $8.0 - 24.0 = -16.0 \, \text{kg} \cdot \text{m/s}$, indicating a momentum of 16 m/s in the direction opposite to A, which is the same direction as B.

Block A, with a Mass of 4