Two blocks of masses 2 kg and 3 kg are placed on a smooth horizontal surface and connected by a light elastic string. When a constant horizontal force of 15 N is applied to the 3 kg block, the steady-state length of the string is 44 cm . When the same horizontal force is instead applied to the 2 kg block, the steady-state length of the string becomes 47 cm . The natural length of the string is _____ cm.

Step-by-step solution

Let the natural length of the string be L₀ and its stiffness constant be k . The acceleration of the system in both cases is: a = F m₁ + m₂ = 15 2 + 3 = 3 m/s ^2 Case 1: The force is applied to the 3 kg block. The tension T₁ in the string is responsible for accelerating the trailing 2 kg block. T₁ = m₁ a = 2 3 = 6 N Using Hooke's law: 6 = k(44 - L₀) Case 2: The force is applied to the 2 kg block. The tension T₂ in the string is responsible for accelerating the trailing 3 kg block. T₂ = m₂ a = 3 3 = 9 N Using Hooke'