A spring with spring constant k = 200 N/m is compressed by 0.1 m. A block of mass 0.5 kg is placed against the spring and released. The block moves along a horizontal surface with a coefficient of kinetic friction μ_k = 0.2. How far does the block travel before coming to rest?

Core Concept

The potential energy stored in the compressed spring is PE = ½kx² = ½(200 N/m)(0.1 m)² = 1 J. This energy is converted to kinetic energy and then dissipated by friction. The work done by friction is W_friction = f × d = μ_k × mg × d. Setting the initial spring energy equal to the work done by friction: 1 J = 0.2 × 0.5 kg × 9.8 m/s² × d → 1 = 0.98 × d → d = 1/0.98 ≈ 1.02 m. This is closest to option C) 1.0 m.