A block of mass 250 g is kept on a vertical spring of spring constant 100 N/m fixed from below. The spring is now compressed to have a length 10 cm shorter than its natural length and the system is released from this position. How high does the block rise? Take g = 10 m/s2.

The height of the block rising is 20 cm


Given


The mass of the block is given as 250 g or 0.250 kg, is placed on a spring constant of 100N/m. The spring’s compressed force is given as 10 cm along with the gravity due to acceleration as g = 10 m/s2.


Formula Used


Using the conversation of energy, we equate the energies of spring compression and potential energy of the mass of the block, the formula of the energy stored in spring compression is



And the energy stored in the block is formulated as



where


The value of spring constant is denoted as “k”, the compression distance is “x”, the mass of the block is given as “m”, the gravity of the block is “g” and the height at which the block is kept is h.


Explanation


Applying the conservation of the mass, between mass of block and spring compression we get the height as:


The equation is as follows:




Placing the values, we get



Therefore, the height is 20 cm


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