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 there 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 10
o 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 problems
If a person with a mass of 50 kg bends over at 60o
T = 0.67 x 50gsin60/sin 10 = 1630 N = 3.3 times body weight
