What height above the point of release will the block reach if air resistance is negligible in the following case:A block of mass 0.21 kg is placed on a vertical spring of constant 3721N/m and...

What height above the point of release will the block reach if air resistance is negligible in the following case:

A block of mass 0.21 kg is placed on a vertical spring of constant 3721N/m and pushed downward, compressing the spring 0.09 m.  After the block is released it leaves the spring and continues to travel upward.  The acceleration of gravity is 9.80 m/s^2.

justaguide | Certified Educator

A block of mass 0.21 kg is placed on a vertical spring with constant 3721 N/m and pushed downward, compressing the spring 0.09 m.  After the block is released it leaves the spring and continues to travel upward. The acceleration of gravity is 9.80 m/s^2.

For a spring with spring constant k, the work that has to be done to compress it by a distance x is given by (1/2)*k*x^2

Here, the spring has a spring constant 3721 N/m and the mass placed on it is pushed downwards by a distance 0.09 m. The energy stored in the system is equal to (1/2)*3721*0.09^2 = 15.07 J

When the spring is released the mass of 0.21 kg that is placed on it is pushed upwards. As the height of a mass m increases by h, the gravitational potential energy in it is m*g*h.

The potential energy in the spring is equal to the gravitational potential energy at the highest point. 15.07 = 0.21*9.8*h

=> h = 7.32 m

The block will reach a height of 7.32 m above the point of release.