A 1-kg box is sliding horizontally along a frictionless surface with a speed of 3 m/s. It collides with and sticks to a 2-kg box that is initially at rest. What is the speed of the boxes after the collision?

Question

BlackTom AI · Accepted Answer

Conservation of linear momentum applies because there are no external horizontal forces and the two boxes stick together (a perfectly inelastic collision).

1) Relevant knowledge points and concepts
- Linear momentum p = m·v is conserved in an isolated system during collisions: total initial momentum = total final momentum.
- In a perfectly inelastic collision (objects stick), kinetic energy is not conserved, but momentum still is.

2) Step-by-step reasoning
- Compute the total initial momentum of the system:
  - 1-kg box: p1 = m1·v1 = 1 kg × 3 m/s = 3 kg·m/s
  - 2-kg box: p2 = m2·v2 = 2 kg × 0 m/s = 0 kg·m/s
  - Total initial momentum p_initial = 3 + 0 = 3 kg·m/s
- After the collision the two boxes stick, so combined mass m_total = 1 kg + 2 kg = 3 kg.
- Apply momentum conservation: p_initial = m_total · v_final
  - 3 kg·m/s = 3 kg × v_final
  - v_final = (3 kg·m/s) / (3 kg) = 1 m/s

3) Intermediate calculation steps (explicit)
- p_initial = 1·3 + 2·0 = 3 kg·m/s
- m_total = 1 + 2 = 3 kg
- v_final = 3 / 3 = 1 m/s

4) Why the correct answer is correct
- Momentum conservation gives a unique final velocity for the combined mass. The arithmetic yields 1 m/s; this is the physically consistent result for a perfectly inelastic collision with the given masses and initial speeds.

5) Why the other choices are incorrect
- 2 m/s: would require total momentum 6 kg·m/s (not true here).
- 3 m/s: would mean the 1-kg box’s speed is unchanged and the 2-kg box gains no momentum—contradicts sticking and momentum sharing.
- 0 m/s: would require initial total momentum zero (not the case).
- "There's not enough information": false because momentum conservation gives a definite answer.

6) Conclusion
The final speed of the stuck boxes is 1 m/s, which matches the provided correct answer.

A 1-kg box is sliding horizontally along a frictionless surface with a speed of 3 m/s. It collides with and sticks to a 2-kg box that is initially at rest. What is the speed of the boxes after the collision?Single choice

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