Step $1$: Define Vector Fields First we would need to define for the upper body of the lifter and the box what the vector fields for weights would be$.$

Let:

$$ upper be the mass of the upper body.

$$ box be the weight of the box.

Consider also that the weight of the lifter's upper body is applied downward with a constant force $$ upper

$$ upper $^.$

Also, the weight of the box acts downward as a constant force $$ box

$$ box $^.$

Motion Work Done Step $2$ The paths of both the lifter's upper body and box need to be considered.

Upper Body Path The path of the upper body of the lifter is $$ upper $().$

Box Path The path of the box is $$ box $().$

Step $3$: Work is Calculated by Line Integral We can use the line integral to compute the work done, Wc$,$ by the back:

$$

$$ Force on the Back The back force $$ back is a $1-$form orthogonal to the radius vector function $(),$ which traverses a quarter circular path.

Let $()$ be the position vector:

$()$

$$ cos $()^+$ sin $()^$ where $$ is the radius and $$ is the parameter from $0$ to $2.$

Calculation of Torque and Force Vectors Calculate the torque $$ as a function of time $$ :

$()$

$()$ back $()$ Then solve for the magnitude of the force vector $$ back $.$