Why people have low back pains

We consider forces in the model of a persons back while lifting an object in the wrong way ie using the back rather than the legs. (here we only a drawing can explain the forces we will see if I can scan one in for you). We have lots of variables so it is useful to make a classified inventory

Known:

Irrelevant:

L, is the only length in the problem so it will cancel from the equations.

Unknown, Uninteresting:

We just want the force on the fifth lumbar vertebra which causes the low back pain so and T are uninteresting for us. We would like to eliminate them in our equations.

Unknown and wanted

, the force on the fifth lumbar vertebra is what we are out to solve for. Important to keep in mind as we build our equations.

We first write the projections of on the horizontal and vertical directions:

There are many ways to solve these equations. We would like to suffering for and T. We choose to square and add the equations to tease out :

We are forced to figure out T which we do from the torque equation which we write choosing the fifth lumbar vertebra as the point of reference:

Putting in numbers we get

These are both enormous forces larger than the entire weight of the whole person so no wonder that after 40 years exerting such forces problems can begin to develop!