A block of mass 4 kg is moving on a smooth horizontal surface with a velocity of 5 m/s. A second mass of 1 kg is gently placed on it. The combined system then collides with and compresses a horizontal ideal spring of spring constant 320 N/m. The maximum compression of the spring is:

Step-by-step solution

First, apply the conservation of linear momentum to find the velocity of the combined mass system after the second mass is placed. Let M = 4 kg, v = 5 m/s, and m = 1 kg. M v = (M + m) V_f 4 5 = (4 + 1) V_f 20 = 5 V_f V_f = 4 m/s Next, apply the conservation of mechanical energy to find the maximum compression x of the spring. The kinetic energy of the combined mass is entirely converted into the elastic potential energy of the spring at maximum compression. 1 2 (M + m) V_f^2 = 1 2 k x^2 1 2 5 (4)^2 = 1 2 320 x^2 5