In a closed system where two objects collide and stick together, how much total $p$ (momentum) does the system have immediately after the collision?

• A. The total $p$ is less than before the collision because some is lost as heat.
• B. The total $p$ is zero because the objects stick together.
• C. The total $p$ is equal to the system's total $p$ before the collision.
• D. The total $p$ is greater than before the collision due to the combination of masses.

Answer: (C)

Verified step by step guidance

1. Recall the principle of conservation of momentum, which states that in a closed system with no external forces, the total momentum before and after a collision remains constant.
2. Identify that when two objects collide and stick together (a perfectly inelastic collision), they move as a single combined mass after the collision.
3. Express the total momentum before the collision as the vector sum of the individual momenta: \(\mathbf{p}_{\text{total before}} = m_1 \mathbf{v}_1 + m_2 \mathbf{v}_2\) where \(m_1\) and \(m_2\) are the masses and \(\mathbf{v}_1\) and \(\mathbf{v}_2\) are the velocities of the two objects.
4. Write the total momentum after the collision as \(\mathbf{p}_{\text{total after}} = (m_1 + m_2) \mathbf{v}_f\), where \(\mathbf{v}_f\) is the final velocity of the combined mass.
5. Use conservation of momentum to set \(\mathbf{p}_{\text{total before}} = \mathbf{p}_{\text{total after}}\), showing that the total momentum immediately after the collision is equal to the total momentum before the collision.