Answer: 5v/3.
- A v/3
- B v
- C 5v/3
- D 7v/3
Correct answer: C. 5v/3
Explanation: Using elastic collision formulas: v<sub>2</sub>_after = (2m<sub>1</sub> x u<sub>1</sub> + (m<sub>2</sub>-m<sub>1</sub>) x u<sub>2</sub>) / (m<sub>1</sub>+m<sub>2</sub>). Take toward each other as opposite signs. Let u<sub>1</sub>=3v, u<sub>2</sub>=-v, m<sub>1</sub>=m, m<sub>2</sub>=2m. v<sub>2</sub>=(2m x 3v + (2m-m)(-v))/(3m) = (6v - v)/3 = 5v/3.
As a pendulum swings, total mechanical energy (KE+PE) stays constant: at the highest points A and C, all energy is potential (zero speed); at the lowest point B, all of that energy has converted into kinetic energy (maximum speed).
Concept context
Work-energy theorem, potential energy, conservation of energy, collisions.