A block of mass 1 kg is attached to a spring with a force constant 100 N/m and rests on a rough horizontal ground as shown in the figure. Initial displacement of block from natural length is 50 cm. The total distance (in m) covered by the block if coefficient of friction between block and ground is 0.05. [g =10 m/s²]

Question

G1 Physics · Accepted Answer

Initial spring energy is E₀=½kx₀²=½(100)(0.50)²=12.5 J. The kinetic-friction force has constant magnitude f=µmg=0.05×1×10=0.5 N. For this data the successive amplitudes reduce to zero after an integral number of half-cycles, so the final spring energy is zero. All the initial mechanical energy is dissipated by friction: fS=E₀ ⇒ S=12.5/0.5=25 m. Hence the total distance travelled is 25 m.