In a two-block system, two blocks collide and stick together. If the initial kinetic energy is $K_{\mathrm{initial}}$ and the final kinetic energy is $K_{\mathrm{final}}$, what is the change in kinetic energy $\Delta K=K_{\mathrm{final}}-K_{\mathrm{initial}}$ due to the collision?

• A. It is zero, because momentum is conserved in all collisions.
• B. It is negative, because some kinetic energy is lost as heat and sound in a perfectly inelastic collision.
• C. It is positive, because the blocks move faster after sticking together.
• D. It is always equal to the initial kinetic energy.

Answer: (B)

Verified step by step guidance

1. Recall that in a collision where two blocks stick together, the collision is perfectly inelastic, meaning the two blocks move together with a common velocity after the collision.
2. Use the principle of conservation of momentum, which states that the total momentum before the collision equals the total momentum after the collision: \(\sum m_i v_{i, initial} = (m_1 + m_2) v_{final}\).
3. Calculate the initial kinetic energy using \(K_{initial} = \frac{1}{2} m_1 v_{1, initial}^2 + \frac{1}{2} m_2 v_{2, initial}^2\) and the final kinetic energy using \(K_{final} = \frac{1}{2} (m_1 + m_2) v_{final}^2\).
4. Determine the change in kinetic energy by subtracting the initial kinetic energy from the final kinetic energy: \(\Delta K = K_{final} - K_{initial}\).
5. Understand that \(\Delta K\) is negative because some kinetic energy is transformed into other forms of energy such as heat and sound during the perfectly inelastic collision, even though momentum is conserved.