A 0 . 5 kg block moving at a speed of 12 ms - 1 compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be _____ Nm - 1

Step-by-step solution

Given: Mass of the block m = 500   g , initial velocity of the block u = 12   m   s - 1 , and final velocity of the block v = u 2 = 6   m   s - 1 . As non-conservative forces are not acting on the system we can conserve energy. Thus, loss in kinetic energy of block = Gain in potential energy of spring 1 2 m u 2 - 1 2 m v 2 = 1 2 k x 2 1 2 × 0 . 5 × 12 2 - 1 2 × 0 . 5 × 6 2 = 1 2 k × 0 . 3 2 k = 600   N   m - 1