The Gravitationa potential energy of the mass (PEG) is given by:

where
m is the mass
g is the gravitational acceleration
h is the heigth of the mass above the reference level (the ground)
In this problem,

and

, therefore the gravitational potential energy of the mass is:
Answer:
The magnitude of force must you apply to hold the platform in this position = 888.89 N
Explanation:
Given that :
Workdone (W) = 80.0 J
length x = 0.180 m
The equation for this work done by the spring is expressed as:

Making the spring constant
the subject of the formula; we have:

Substituting our given values, we have:


The magnitude of the force that must be apply to the hold platform in this position is given by the formula :


F = 888.89 N