Physics

To solve this problem, we can use the conservation of mechanical energy. The block starts with gravitational potential energy at height and converts this energy into the potential energy of the spring as it compresses the spring.

 

Write down the total mechanical energy at the starting point

The block starts with gravitational potential energy given by:

where:

is the mass of the block,

is the acceleration due to gravity,

is the height.

 

At the point where the spring is maximally compressed, all of the gravitational potential energy is converted into the potential energy stored in the spring.

 

Write down the potential energy stored in the spring

The potential energy stored in the spring at maximum compression is given by:

where:

is the spring constant,

is the maximum compression of the spring.

 

Use conservation of energy

Since mechanical energy is conserved (no friction or other energy losses), the gravitational potential energy at the start is equal to the spring's potential energy at maximum compression:

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