A block of mass 2 kg moving with a speed of 4 m s ⁻¹ on a frictionless horizontal surface collides elastically with an identical block initially at rest. The second block is attached to one end of a relaxed ideal spring of spring constant 32 N m ⁻¹ , with its other end fixed to a rigid wall. The maximum compression of the spring is:

Step-by-step solution

Since the collision is perfectly elastic and the blocks have identical masses, they exchange their velocities upon collision. Velocity of the second block just after the collision, v = 4 m s ⁻¹ . By conservation of mechanical energy for the second block and spring system: 1 2 m v^2 = 1 2 k x^2 Substituting the given values ( m = 2 kg, v = 4 m s ⁻¹ , k = 32 N m ⁻¹ ): 1 2 2 (4)^2 = 1 2 32 x^2 16 = 16 x^2 x^2 = 1 x = 1 m. Answer: 1 m