# Back damage

In the section on vectors we looked at the tension in your back muscles when you bend over. One assumption that was made was that the reaction at the pelvis acted long the spine. If this is not so then we need to use the principle of moments to work out the tension in the back muscles.

Let's consider somebody bending over at an angle A to put a heavy case into the back of a car, probably one of the worst lifting situations.

Let the mass of the upper body of the person (about 2/3 total body mass) be W, the reaction at the pelvis be R acting along a line q to the spine (Figure 1) and the load that the person lifts be mg.

Taking moments about the base of the spine (P) gives:

TL sin 10 = (W + mg) L cos A

And so:

Tsin 10o =(W + mg) cos A

Notice that since the line of action of the reaction at the pelvis (R) runs through the point P here is no moment of S about P.

Example problem
A gardener of mass 80 kg lifts a mower of mass 50 kg into the back of their truck. In doing this they lean over at an angle of 60o to the horizontal. (g = 9.8 ms-2)
Calculate the tension in their back muscles.

Tsin 10o = (W + mg) cos A      T sin 10 = 130xgxcos 60
T = 637/sin 10 = 3668 N

## Bending over and damage to your back – an alternative approach

You probably know that the correct way to lift something is by bending your knees and keeping your back straight. The following calculation shows very clearly why this is!
This can be demonstrated very well by using a mop to represent the spine and a string to represent the back muscles!

Consider a person bending over so that their spine makes an angle of A with the horizontal (see Figure 2).

Their back muscles make an angle of 10o with the spine and have a tension T. We will assume that the reaction (R) at the pelvis acts along the spine. It has been calculated that the weight of the upper body (W) is about 2/3 of the total body weight.

Resolving at right angles to the spine we have:

W cosA = T sin (10)

Example problem
If a person with a mass of 50 kg bends over at 60o then

T = 0.67 x 50gsin60/sin 10 = 1630 N = 3.3 times body weight