Answer: 0.2 m.
- A 0.1 m
- B 0.2 m
- C 0.4 m
- D 0.5 m
Correct answer: B. 0.2 m
Explanation: Energy: mgh + mgx = (1/2)kx2. 2x10x2 + 2x10xx = 500x2. 40 + 20x = 500x2. 500x2 - 20x - 40 = 0. 25x2 - x - 2 = 0. x = (1 + sqrt(1+200))/50 approx 0.2 m.
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.