A block of mass 1 kg is initially at rest on a smooth horizontal surface and is attached to a relaxed ideal spring of force constant 30 N/m . A variable horizontal force F = F₀ - x (where x is the extension of the spring) is applied to the block in the direction of the extension. If F₀ = 20 N and = 10 N/m , the maximum kinetic energy acquired by the block is:

Step-by-step solution

The block acquires maximum kinetic energy when its speed is maximum. This occurs when the net force acting on the block becomes zero. The forces acting on the block in the horizontal direction are the applied force F and the spring force F_s = kx acting in the opposite direction. Net force, F_ net = F - F_s = (F₀ - x) - kx For maximum kinetic energy, F_ net = 0 20 - 10x - 30x = 0 40x = 20 x = 0.5 m According to the work-energy theorem, the change in kinetic energy is equal to the work done by the net force. Since t