Question Detail
Question
A 0.40 kg block slides across a horizontal frictionless surface at 0.50 m/s and compresses a spring with k = 750 N/m. When the block is momentarily stopped by the spring, what is the compression distance d?
Correct Answer
Option A is the correct answer.
Detailed Explanation
Initial KE of block = ½ × 0.40 kg × (0.50 m/s)² = 0.5 × 0.40 × 0.25 = 0.05 J. This converts entirely to spring PE at maximum compression: ½ k d² = 0.05 J. So, d² = (2 × 0.05) / 750 = 0.1 / 750 = 1.333 × 10⁻⁴, and d = √(1.333 × 10⁻⁴) = 0.01155 m = 1.15 cm.
Hint
Use conservation of mechanical energy. The kinetic energy of the block is transformed into elastic potential energy of the spring.