A block of mass 250 g is placed on a vertical spring with a spring constant of 100 N/m that is fixed from below. The spring is compressed so its length is 10 cm less than its natural length, and the system is released from this position. Calculate how high the block rises. Take g = 10 m/s ^2 .

Step-by-step solution

Let h be the maximum height the block rises from its initial compressed position. According to the law of conservation of mechanical energy, the initial elastic potential energy of the spring is converted into the gravitational potential energy of the block at the maximum height. 1 2 kx^2 = mgh Given: m = 250 g = 0.25 kg k = 100 N/m x = 10 cm = 0.1 m g = 10 m/s ^2 Substituting the values into the energy equation: 1 2 100 (0.1)^2 = 0.25 10 h 50 0.01 = 2.5h 0.5 = 2.5h h = 0.5 2.5 m h = 0.2 m = 20 cm