A light spring with a spring constant k is fixed at one end ...

Question

A light spring with a spring constant k is fixed at one end to point O, while the other end is attached to a block of mass m. Initially, the block is at point A, located on the same horizontal level as O, with the spring at its natural length L. The block is then slowly moved downward until it reaches point B, where the spring is vertically stretched and at rest. Assuming no air resistance, what is the work done by gravity on the block when it reaches point B?

Here's how to approach calculating the work done by gravity on the object as it moves from point to point .

Forces at the equilibrium position :

At the lowest point , the spring is stretched, and the forces on the block are in equilibrium:

where:

is the spring constant,

is the extension of the spring from its natural length ,

is the gravitational force.

From this, we solve for the extension:

Total vertical displacement from to :

At the lowest point, the total length of the spring is:

Work done by gravity:

The work done by gravity is the product of the gravitational force and the total vertical displacement:

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