Question Detail
Question
A 10-kg box moving at 5 m/s on a frictionless surface runs into a light spring of force constant 100 N/cm. What is the maximum compression of the spring?
Correct Answer
Option B is the correct answer.
Detailed Explanation
First, convert k to N/m: 100 N/cm = 10000 N/m. Initial kinetic energy = ½ × 10 kg × (5 m/s)² = 125 J. At maximum compression, all KE is converted to spring PE: ½ k x² = 125 J. So, x² = (2 × 125) / 10000 = 250/10000 = 0.025, and x = √0.025 ≈ 0.158 m = 0.16 m.
Hint
Use conservation of mechanical energy. The initial kinetic energy becomes elastic potential energy at maximum compression. Pay attention to unit conversions for the spring constant.